How are you trying to upgrade? Are you following the instructions on this Apple Support page -> How to download and install macOS - Apple Support?
I suggest upgrading to Catalina first then after making sure all is working correctly in Catalina, upgrade to Monterey. There were very significant architectural changes in macOS from High Sierra to Mojave to Catalina including major changes/improvements in APFS and the loss of 32-bit app support. Even further changes between Catalina & Monterey.
Is the system drive in your 2015 MBP already formatted as APFS or is it still MacOS Extended Journaled?
The "Recover Server could not be contacted" error is a known bug in downloading High Sierra (and there is a workaround if you need it). If you are getting this message when trying to download later versions of macOS it may be just a temporary problem ... try again another day. BTW, if you are using WiFi to do this, don't. Use wired ethernet instead.