I am a bit confused by your setup. Is this a home network? Is it an enterprise setup?
Your title asks about routers yet your text only talks about servers.
Do you have redundant internet connections? Multiple routers? Failover? High Availability servers?
If you have a single internet connection and a single router and are worried about one server going bad and needed to be rebooted, just install the VPN server on the router. No need for another server.
There is a huge difference between having a password and being secure. VPN servers are security hardened and tested to resist attacks. They have a tiny attack surface. OTOH, most services that are supposed to run on a LAN are not nearly as secure, come down with security exploits on a regular basis and are generally built for convenience, not security.
I am pretty sure enterprise users of OOB services run those on separate networks altogether so that common (trusted) users on the general network don't have access to them.
BTW, I am not sure what you are trying to do exactly, but if it's to reboot a machine when it stops responding, you'll find programmable PDUs like this guy that can power cycle a machine controlled remotely or have various types of tests decide to power cycle said machine. They are meant to reboot network infrastructure, but can work just as well with servers.
https://www.amazon.com/Web-Power-Switch-Pro-Model/dp/B0765NCB2L
I used the Digital Loggers Web Power Switch for some testing I was doing for work. It's pretty pricey, but it allows you to turn the switches on with some pretty short cycle times. On order of seconds. There are some hacks to the firmware you can do to make the cycle time ridiculously short (around 100 ms or so). In our testing I was cycling the outlets around 10 times a second (yes, this would probably cause the relays to fail really quick, but we didn't care for the tests). It's scriptable, so you don't even need a smart setup, just a script you run when you need it.
The Tripplite guide was perfect for explaining the different types of PDUs! I am now looking at this one as it seems to have individual switch control and a web interface, which is exactly what I'm looking for. I'm not sure if I will be able to SSH into it though, which may make it unusable to proxmoc so I will have to confirm that first.
This is the best, most programmable option:
https://smile.amazon.com/Web-Power-Switch-Pro-Model/dp/B0765NCB2L/
It's rock-solid, supports a pile of protocols for remote control and is also capable of monitoring the internet connection and do all kinds of sequences in response to a connection issue.
I have 2 I use on my whole networking gear closet to be able to reboot things remotely.
https://www.amazon.com/Web-Power-Switch-Pro-Model/dp/B0765NCB2L
Not the same price but a lot more configurable using a lot of different protocols.
And it has a "restart" manual command :-)
https://www.amazon.com/gp/product/B0765NCB2L/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
I went with this as i wanted something not web based, mountable to the back of my TV stand, and had a few ports so that i can plug in most of my home audio stuff and my modem.
My ISP likes to knock me offline in a way where my internet connection drops BUT my modem doesnt actually go offline. Only forcing the modem to reboot brings me backonline.
I was able to use the above and set up a ping to google for that port and now my modem reboot as needed.
Web Power Switch Pro Model https://smile.amazon.com/dp/B0765NCB2L/ref=cm_sw_r_apan_glt_i_NN7ZM013N832NKGN8ATQ
Web Power Switch Pro Model https://www.amazon.com/dp/B0765NCB2L/ref=cm_sw_r_apan_glt_fabc_J067GHX04REJEH5234BE?_encoding=UTF8&psc=1
Not cheap but has way more options too.
I used one of these asset work to control our lab's components. It may be useful to you. https://smile.amazon.com/dp/B0765NCB2L/ref=cm_sw_r_cp_apa_fabc_mK59FbJK6H80Z
This was recommended in thread, https://www.amazon.com/Web-Power-Switch-Pro-Model/dp/B0765NCB2L/
You don't think that would work?
Not cheap, but that's what you want.
Fully standalone and capable of all kinds of other protocols and also scripting the turn off/on sequence...
https://www.amazon.com/Web-Power-Switch-Pro-Model/dp/B0765NCB2L/
Seems to require a USG or UDM. That's disappointing.
Hopefully, all sockets are independently (and manually) controllable.
More flexible (but black!) competition:
Digital loggers makes some https://www.amazon.com/dp/B0765NCB2L/ref=cm_sw_r_cp_apa_i_ac-tFbK6976M6
https://www.amazon.com/Web-Power-Switch-Pro-Model/dp/B0765NCB2L/
There are cheaper options if you look around, but that's what you need in general.
Kind of pricey, but this could meet your needs:
https://www.amazon.com/dp/B0765NCB2L
Can be configured to ping a device and initiate a reboot if no response. You can also remote into the power switch to initiate reboots or shutdowns. They have a demo portal set up so you can play with admin features, http://pro.digital-loggers.com, user/pass admin/4321
Less expensive options include:
https://amazon.com/dp/B015NM0LKI - two outlets
https://amazon.com/dp/B01GOOE8OY - single outlet
I don't have first-hand experience with any of the devices, I had been looking into this issue myself a while back and found these devices after some light research.
This might be overkill but if you have a lot of rigs, this is an option.
While I'd love to have something within the UniFi pane of glass to automatically cycle cable modem/router/etc., I think this offering falls well short.
Although 4x the price, sticking one of these in between the UPS and the devices works quite nicely. The only thing missing is actual consumption logging (and a different overall form factor would be nice too).