Upgrade RestSharp to v107

[szyb]

I thought it would be upgraded during the .NET 6 upgrade (#258) but this version (v107) contains quite a lot breaking changes described at: https://restsharp.dev/v107/#restclient-and-options
Need to focus on that, because this library is the core of the whole website

Edit: This task is important and it will take a while to implement this. So maybe we consider switch to HttpClient directly? We will get no more upgrades and that is why this might be a great idea. The amount of work would be the same.

[szyb]

consider also adding header If-Modified-Since for every GET request