denyasis: So, just to clarify, what features are dependant on the galaxy client?
I'm just going to assume you're asking about single-player features, since it should be obvious that no multi-player functionality will work without Galaxy.
1) There is a system of "milestones" that you achieve by completing certain tasks - for example: earning money, walking on planets, learning words in an alien language, destroying sentinels (also pirates), surviving in harsh environments, and others. There are two NPCs in the nexus which will give you rewards for reaching these milestones and for discovering planets, minerals, plants, and animals. In past versions of these games, these bonuses were handles by Nada and Polo. After the nexus was created (in the Beyond update), these were moved to Ares and Helios. Without Galaxy, Helios will only work ONCE and Ares will never work. Note that these USED to work in single-player (offline mode), and there is no specific multi-player aspect to them, but it now requires an internet connection for them to function correctly.
2) There is a shop where you can purchase items with "Quicksilver". Without Galaxy, or editing your save game (or using a mod), this shop has virtually nothing in it, and even with the mod (or using the save game editor), there is virtually no quicksilver to be had, because the offline means of acquiring it are extremely limited.
3) Almost an entire update (living ship) is meaningless without Galaxy, as you won't have access to the living ship egg required to make use of this update. With a save editor (or the mod), you can find it in the quicksilver store, but without using the editor to cheat yourself a large amount of quicksilver, you won't be able to actually buy one.
4) There are quests which cannot be solved - you can encounter NPCs that ask you to take actions (e.g. placing message buoys) which the game will NOT allow you to build unless you're online. Without the ability to do this, you cannot complete the quest, and you'll be stuck with it unless you abandon it. I wrote "quests", but in fairness I only personally know of that one, but there may be more. After getting stuck with a quest it was literally impossible to solve, I stopped interacting with crashed NPCs, so if there are more, I haven't run into them.
5) There are various quests available which do provide quicksilver, and although they are normally associated with online play, they are not explicitly associated with multi-player play, since many if not all of them can be completed solo. I have yet to find any of these quests, presumably because I'm not running the game via Galaxy.
While none of these individually is enough to seriously detract from the game, they are symptoms of a larger problem where Hello Games is trying to force the player to maintain an online-connection in order to play, even when the player is in single-player mode. GoG has responded to complaints by pointing at that it supposedly says somewhere on the game description page that some online features require an internet connection. This is untrue. The truth is that ALL online features require an internet connection, since that is LITERALLY the definition of an online feature. Anyone telling you that "some" online features require an internet connection is obviously either stupid or trying to hide the truth.
The truth that they're hiding is that certain single-player (non-multiplayer) features require an internet connection, and there is absolutely no logical reason that these single-player features should be online features... except that they're trying to push you into maintaining an online connection and force you into using either steam or GoG's steam wannabe - Galaxy. These features do not require an online connection because they were part of the game prior to the Beyond update and worked fine without one.
edit: To be clear, I mean that that while these features DO require an online connection, there is no
inherent necessity for it, unlike the obvious necessity of an online connection if you want to play with other friends or visit other people's bases. The necessity is artificially added by Hello Games, and not an intrinsic aspect of the feature.