It just feels like I'm talking to someone unnecessarily combative, abrasive, and defensive is all. Like I'm talking to somebody's ego who is ready to posture and peacock and fight others who are trying to help. We are not enemies!

You keep conflating what a router does vs. what a switch does, and I find that confusing. (Specific example: you mixed up a TP-Link router with a Netgear switch above. One is a router and one is a switch.)

For the sake of clarity, I'll try to rephrase your asks, and you can either confirm I read you correctly, or you can reply with more detail and clarification. That way we can correctly match solutions to your identified problems.

Here are the problems you have identified, and again, please correct me if I'm not reading you correctly:

Problem 1: Want the ability to connect multiple client devices to the same LAN. User is currently manually connecting and disconnecting ethernet connection for each device for work fetch/flush. User currently uses 1 PC for personal use and 3 PCs as dedicated crunchers, for a current total of 4 client devices.

Solution: Any switch will work. Consider at least an 8-port switch in case needs change in the future, since a 5-port switch will be maxed out if you buy one now.
Most if not all consumer grade routers incorporate a 4-port (or more) switch for its LAN interface built-in. So you could potentially connect all 4 client devices to the LAN switch ports on your existing router. You always have the option of buying a separate switch that meets your needs, wants, and budget. We all have personal preferences, and sometimes needs vary greatly. E.g. if you want a more complicated network architecture with a bunch of VLANs (for security by isolation reasons), then an unmanaged ("dumb") switch won't work, and you'll need a VLAN-aware switch. E.g. at least a consumer-grade "Smart" or "Plus" switch which might also be known as Layer 2+ switch. If you need more 802.1x port security and other security features, you'll have to choose a switch that meets those requirements. For cheap switches, I recommended the Netgear small business/consumer line of switches that specifically have the lifetime warranty since I've had a good experience. As I type this right now, my connection goes through 3 Netgear switches and 1 ZyXel switch. My recommendation for the switches with lifetime warranty is just my personal preference that lifetime warranties can be very helpful vs. the standard 1 year warranty. But this is neither here nor there: buy whatever switch meets your needs, wants, and budget. The point is the switch is the network device that connects multiple other devices on the same network segment. It sounds tedious and unnecessary to not use a switch and manually connect/disconnect devices. Life is too short for that.

Problem 2: User wants the ability for multiple client device traffic to traverse a single VPN connection to a 3rd party VPN provider without having to manually connect each client device to its own VPN connection, which are often limited in quantity depending on the 3rd party provider's plans.

Solution: Terminate the 3rd party VPN connection for the entire household on the router, which would only use one VPN connection to the outside world.
In the past, I've terminated a 3rd party VPN connection on my DIY pfSense router since I really love the advanced features and the free, open-source (at least at the time) nature. I won't get into the pfSense vs. OPNsense fork debate, since that's tangential to the point I'm trying to make. But fortunately consumer-grade routers have also started implementing VPN client features over the past 10 or so years, which is great news. In the past, many COTS routers only supported ancient VPN server termination like the obsolete/insecure PPTP protocol to connect from the outside world (e.g. when traveling) to your home router. But many modern COTS routers allow for VPN client configurations specifically for a 3rd party VPN service, and many support not just the gross IPsec but OpenVPN and now Wireguard protocols. The downside, from what I've observed so far, is that consumer grade manufacturers vary greatly on how responsive they are for security/firmware updates. I've had excellent experience with Asus COTS routers since their AsusWRT (based off OpenWRT) is a platform they can easily apply to multiple SKUs and thus provide years of security/firmware/bugfix updates. My RT-N66U for example is long EOL but still got security updates in 2025. So if going consumer grade off-the-shelf, I can vouch for Asus firmware. Just be sure to read reviews, since sometimes they do release lemon routers that perform poorly and are unreliable, so make sure to choose a good one that meets your needs. But at least with AsusWRT there will be a place to terminate the client side of your 3rd party VPN connection. I personally recommend against TP-Link and Netgear routers since in my experience they don't emphasize timely security updates and long-term support. They seem to abandon their products quickly, and I'm biased against those two brands for COTS routers. If you're an advanced user and want lots of cool features, I do recommend going the pfSense (or OPNsense) route, as long as you are aware of the big learning curve and many dozens of hours tweaking configs and playing with packages. But this is a huge leap and out of scope for the simple need to connect to a 3rd party VPN service with just one client connection. [Edit: If you're a semi-advanced user but don't want the complexity of something like pfSense/OPNsense but want a bit more than consumer grade stuff, then check out the Firewalla line of routers. I'm playing with one in transparent firewall mode and it's very pretty, but the downside is they are heavily focused on managing the router via a phone app instead of a normal local web interface. But the feature set they provide is excellent, and they seem very responsive to feedback and consumer wants and needs. They reply even on weekends and I've had them reply at like 3-5 am multiple times and provide a beta firmware that fixed something. Like holy moly they go above and beyond on the customer service area! So that's fantastic. Another company that is very popular for semi-advanced features and a pretty UI is Ubiquiti, specifically their UniFi line of routers. Lots of advanced features and great for the nerdy home user or small business. I'm pretty sure all their routers also support OpenVPN/Wireguard client configs, but double check.]

I hope I've adequately understood the problems you asked, and I hope I've communicated solutions to you. Basically buy a switch for the physical connectivity, and buy a router that supports client VPN connectivity. Then BAM! You can set it and forget it. This is how I run my shop, and it's lovely. I can focus on life things instead of babysitting BOINC/WCG crunchboxes. As far as specific makes and models of routers and switches, that completely depends on your needs, wants, project requirements, technical ability, and budget.

Edited to add: This should go without saying since I hope it's common sense, but please don't make the mistake of thinking a router <$100 will have the CPU horsepower to deliver good VPN throughput. To meet that price point, they put in lower tier CPUs/SOCs and other components, and they can barely handle NAT/SPI routing, but asking it to do real-time encryption/decryption of an OpenVPN or even Wireguard VPN connection will bring your Internet speeds to a crawl. But a lot of this also depends on your current Internet speeds and expectations. Just fair warning that if you for example want 100 Mbps, 200 Mbps, 500 Mbps or whatever Internet speeds over VPN, you're going to have to buy a router with a beefy enough CPU to handle that overhead. So I'd plan on buying a decent enough router that will for sure meet your needs and expectations.