A piece of software always runs locally. It is in some cases those who needs to communicate with the server fail to deliver the usual function you expect when offline.
Please do not confuse one to another.
And perhaps you can start by complaining which services you are using heavily rely on the server side? General questions attract general answers and IMHO you are better off just search on the internet.
And I heard Figma is a heavy adopter of WebAssembly which could be faster when running not in a wrapper like Electron. Since it is WebAssembly one can imagine the so-called “desktop version” has to be also WebAssembly and it has to have a wrapper around it.
If all these are true, OP just need to find a way to load the fonts into the web version.