Historically the process was known as ROM ripping (and yes it gets confusing when people rip an optical disc) but we have not really seen it employed much since the early days of the DS (here is me in 2005 with a thread on the matter --
https://ezflash.sosuke.com/viewtopic.php?f=10&t=457 ) or PSP. This is mainly as historically languages were a lot of the game but today 3d models, video files and the like take up the bulk of the game -- despite a few advancements in text engines (or at least such advancements becoming commonplace) 100000 words/game scripts take up about the same amount of space. On top of this where games might have once been "multi5" in Europe they tend to be monolingual today if they do contain lots of voiced audio (while music takes up less than video it is still not nothing).
Three main approaches, and an extension of the concepts.
1) You delete files. If the game never accesses them, never accesses them in any way you care about (while we may debate about having not properly played a game if I never defeat the end boss then fewer will make the case if I never stay for the credits, or maybe watch them online) or has decent "can't find file, won't just crash" coding then win here.
2) You relink the files. No tools I am aware of for the Switch do this, indeed PC iso formats and the PSP are going to be the only ones I can link to so as you can do it with simple clicking as opposed to manually going through files/file systems changing pointers. Anyway the idea is if deleting a file is going to make it crash or at least behave badly you find a suitable replacement and rather than just overwriting it (50 megs is still 50 megs and if you have 5 copies needed...) you point at the original location for all instance you want to repoint.
3) You build minimal files or employ compression. A basic relink might get you something but if the game only needs the header and an utterly basic example of the file (say an audio file needs the audio header and a sample length of silence then that might still be significantly smaller than the smallest audio track). The devs might not have bothered to employ compression, or decided the increased load times were too great a cost where you might value the space more than a few seconds more loading. How easy this is varies with the system; the PSP could do it trivially at iso level (see CISO and Umdgen, also want umdgen for relinking), various aspects of the DS can do it more easily as it is more or less there in all and other aspects of the DS would be a full bore ROM hack to handle, for the GBA it would likely be pointless at game level owing to a lack of file system but at flash cart level it was done by some even if the gains were mostly the same as ROM trimming). More advanced than this would be reducing quality of textures, audio quality (if some audiophool dev or their customers demanded uncompressed dolby or similar, which we did kind of see on the PS3 for a hot moment, then change for perfectly acceptable MP3 or something and that changes sizes dramatically. I tend not to see this unofficially outside of CD based system emulators allowing MP3 for audio tracks or maybe a handful of people going down the extreme low settings path (half life and its sequel had some fantastic examples here, though quake is probably the earlier example) but devs do it all the time (see downloadable/optional texture packs for some games).
The extension comes in splitting the game. For the DS this was most notably done with Sonic Rush wherein you would make a ROM play one half of the levels, then delete the ROM, carry the save and play the other half of the levels. Others have done this for games where only the minigame is wanted or if it is a game collection then only an individual game is wanted.
As far as game updates then as far as I am aware they are just another archive format so you can pull them apart and poke at the innards much the same in the end, don't know how much is outright file replacement and how much is a delta.
In the end though this is current year so it is likely easier to just buy a USB drive (whether you have to also change custom firmware I don't know, and don't much care) or buy a bigger SD card. Failing that you could call it a pirate syndrome preventative measure.
