Welcome back I guess.
Other than the passme stuff nothing was ever blocked for the DS and DS lite. All DS cards are then as you describe, give or take what you feel about updating the onboard firmwares of some of them (usually throw it on, hold a button while booting, wait for it to be done, maybe repeat if it is a chain of updates that need doing).
It was only the DSi and 3ds with readily updated firmwares that frustrated DS flash carts. The 3ds stuff is somewhat lessened these days if you hack it and use older versions of the DS compatibility layer (not sure if they have blown it right open yet but eh). DSi also has a measure of this but DSi hacking is slightly more involved. Any neither are my area and it does not seem to be the case here.
Hardware limitations prevent GBA code from being run properly from a DS slot. There are three cards that do any measure of good GBA emulation by virtue of being crammed full of extra hardware to emulate it onboard, though for most purposes it is the supercard dstwo (hard to find nowadays) and its successor aimed more at the 3ds in the supercard 4 in 1 aka DSTwo plus that serves here. Naturally said extra hardware gobbles a bit more power, and pumps the price up a bit. For the sake of completeness the others are the iplayer (supercard's attempt at a more legit flash cart and lacked much in the way of commercial support, not sure what goes nowadays) and ismart mm (a vendor site bought the design for the iplayer and crammed an older version of the dstwo firmware onto it, also got a version of dingux* a bit later in time which also returned for the DStwo a bit later still. The owner of the vendor site then died which pretty much stopped that one).
Said emulation is not flawless, and homebrew emulators are even more of a grey zone (in some ways they are less demanding, in other ways the emulators on said cards have their fixes optimised for the commercial games) but looking at your posts then sounds like you have an EZFlash Omega to play with so I will skip that one.
*could manage about 15fps if you were lucky PS1 emulation. Don't get one for it though.
Said DSTwo is probably also the cream of the crop for commercial DS games. We do have standalone libraries of patches these days though so most shortcomings can be made up there. The main things to rise up to match it would be the Wood firmware made for old school R4s and a few others (cloned, usually badly, by more people still) and AKAIO for the acekard 2i.
Most other flash carts (M3, the various EZ5 lines and a few others) tapered off and were finished when the DSi/3ds updates got serious and took out most things of the time. It was still pretty late in the day and not much was released afterwards (a handful of pokemon games being the main ones as far as most are concerned). Again though
https://gbatemp.net/threads/ap-patch-preservation.477536/ and stuff like it exists so stuff can still get done.
Of the "current" non Supercard DSi/3ds lines that most shops stock it should be noted that several feature so called timebombs wherein they refuse to work with the stock firmware after a system date. Winding back the date or using an alternative firmware is an option but personally I would not go there to begin with. Afraid I am not up to date and what it doing what nowadays -- you were probably still around to see the term R4 become the generic term for flash cart with a thousand different things with R4 in the name... it got worse.
Emulation on the DS somewhat stagnated as time went on, and then all but died (give or take some efforts with GB/GBC emulation) with the rise of IOS and Android. Where the GBA era was all hopping with top notch code and people getting crazy features for a handheld going on this was more limited on the DS, many of the top tier coders of the GBA era stuck around and got some good stuff going on but it was perhaps not quite as inventive. You can get a lot done though and I look favourably back upon it compared to what we saw on the 3ds and are seeing now on the Switch. In terms of pure playability the PSP has the DS beat but you can certainly enjoy much of the SNES (oh the DSTwo also has enhanced SNES abilities as well, even touching some of the special chip stuff), megadrive and mainstream older consoles on it, including some perks for keyboard sporting "minicomputers" by virtue of having a touchscreen.
"needing a GBA slot"
There was some homebrew that took advantage of the extra memory some GBA slot cards (and libraries to support them) offered. Emulation wise then
https://wiki.gbatemp.net/wiki/3_in_1_Expansion_Pack_for_EZ-Flash_V#Third-Party
So rumble in those GB/GBC games with it, and a minor quirk for some SNES games.
If you are still thinking needs flashme or a nopass then don't worry about that. That was more or less over by mid 2009 (and long before then it was a "holdout" type position), and these days the EZ4 (about the only thing to stick around in some capacity and thus the only thing of that era of any merit you stand a decent chance of finding for sale) does not even have a DS mode on newer firmwares and revisions. The EZ Omega and Everdrive stuff does not have any appreciable DS functionality really either.
Anyway I am waffling.
Short version.
If you don't mind the expense and power drain then the DSTwo/DSTwo plus are good stuff. Loads of nice features for DS ROMs, enhanced emulation on various fronts, some abilities to run GBA code as part of that, media player that plays many normal media files...
Something that supports the wood firmware is a good choice. Do note the original R4 which is supported by it is still limited to SD family stuff (2 gigs or less). As it is largely based on the same code then the acekard 2i is also worth noting in this, the build quality is occasionally a bit suspect there (enough to note in this) but can usually be worked around.
There are various things named R4. I have not kept up here (at one point it was the R4i Gold that was the main thing here but again I am some time out of the loop) and timebombs make me both wary and sad so read further there. These tend not to have as many features but will have cheats, ability to run commercial games and homebrew which I find is all most people care about.
If you are willing to fiddle with the extra patches then a lot of things have nice options too -- the EZ5i is probably as close as you are going to get feature wise to the DSTwo (indeed its in game text reader is probably better than the DSTwo's, savestates maybe only slightly worse). The ismart MM was dropped before that but feature wise... it is a version of the DSTwo firmware, albeit older. I don't know if I would particularly suggest the later M3 lines here (we will skip the Sakura and Moonlight drama) but you could get some things done.
If your interest is purely homebrew then anything that has a DLDI patch (which should be just about everything, and all but the very very first DS slot things should do it automatically, to say nothing of there being DS side code to handle it if you care) should be good here.
like a 250 dollar kit back when DDR4 was Intel only