Kamul: I don't know how user-friendly Vortex is, but I didn't have the best experience in the past, sicne it seemed to be capped to non-premium Nexus users. I wonder if that's still the case, or if MO2's compatibility for GOG version is even planned.
What's capped is the download speed for nexus downloads. And that also applies to downloads through MO2 (or your browser).
The main difference between MO2 and Vortex is their deployment method. I find managing big load orders a lot easier in MO2 than in Vortex. But given the fact that most SKSE-based plugins don't work with the GoG version (some people say 'yet', others who are less pessimistic, or more informed, say 'most of them probably never will'), your Vortex load order isn't probably going to be too big, anyway.
Kamul: So, before I make the decision of adquiring a DRM-free copy of Skyrim for modding purposes: is this version of the game compatible with Mod Organizer 2?
Whether or not the GoG version is supported by MO2 shouldn't be you main concern. Eventually, it will be supported. What's more of a big deal when it comes to modding is the fact that the GoG version is a different build of the game compared to the Steam version. And because of the changes made to the GoG version (no Steam DRM, removal of Creation Club etc.) it will probably never be fully cross-compatible with whatever is the latest build on Steam. That means two things: all modders doing more sophisticated modding of the main executable have to maintain special versions of their mods for the GoG version and in order to do that, they have to have access to the GoG version in the first place.
Meanwhile, quite a few essential SKSE-based plugins haven't even been updated to Anniversary Edition (1.6.x), so if you want maximum mod compatiblity, you do a rollback to version 1.5.97 on Steam (the last version before the release of AE back in November '21). For obvious reasons, that's not going to be possible with the GoG version, even though theoretically, GoG supports easy rollbacks.
To sum it up: as things are now, even though the GoG version should be superior to the Steam version due to the removal of Steam DRM and the Creation Club and the update and rollback capabilities that GoG offers, it's clearly inferior to the Steam version for about 95% of all potential buyers.