I use a plain LibreOffice Calc sheet, an equivalent of Excel, but much lighter and system-agnostic.

In it, I track all the things I have, the partial completion percentage for each "group" (GOG, PS2, physical PC games, etc.), total completion percentage, somewhat when I finished each game (there's stuff I finished years ago, which makes pinpointing dates a tad hard), and a few other small data.

The partial completion percentage also helps to pick the games from the groups I've been neglecting the most (the ones that end up with the lowest percentages).

If you want to use LibreOffice sheets too, I think there is a port of LibreOffice to Android, and if you install Linux on Android, it works there too.

I use Backloggery

I use Gamefaqs and MobyGames to track my collection. On Gamefaqs there's a lot of ways to categorize games like digital/physical and played/finished and more. MobyGames looks nice and both of these are games database websites so they also have tons of other info so I also just browse and find info about various games/companies/people etc.

I also use HLTB, I don't think I do a lot of managing from mobile, only from desktop.