After talking some talking and research myself, romscout, and NOVel have decided that any runs done on flashcart with GBA slot should be marked as emulator runs given the apparently load advantage along with the new advantage of GBA slot on being available on them.

What kind of research are we talking about? I just spent like an hour to time some loadings (randomly chosen) from 4 any% runs on leaderboards (AANXAAN's, Romscout's, mine and Strizer86's (I couldn't download Frozer's one because it is on Twitch)) which are done on different platforms and 2 flashcart runs just to see if there's any difference. Videos I downloaded were 30fps while game runs at 60, so if you double the frames I counted at 30fps you get approximate number of frames in 60fps (I added them in brackets after 30fps number) and here's the result:
Loading before the first room in The Lost Village
AANXAAN – 6(12) frames DS emu
Romscout – 8(16) frames DS
Diagon – 8(16) frames 3DS flashcart
Strizer – 9(18) frames 3DS flashcart

Loading before cutscene with Yoko and Julius
AANXAAN – 4(8) frames DS emu
Romscout – 6(12) frames DS
Diagon – 6(12) frames 3DS flashcart
Strizer – 6(12) frames 3DS flashcart

Loading before entering Demon Guest House
AANXAAN – 5(10) frames DS emu
Romscout – 6(12) frames DS
Diagon – 7(14) frames 3DS flashcart
Strizer – 8(16) frames 3DS flashcart

Loading before entering Pinnacle
AANXAAN – 5(10) frames DS emu
Romscout – 6(12) frames DS
Diagon – 6(12) frames 3DS flashcart
Strizer – 7(14) frames 3DS flashcart

Loading before reentering Demon Guest House
AANXAAN – 7(14) frames DS emu
Romscout – 8(16) frames DS
Diagon – 9(18) frames 3DS flashcart
Strizer – 10(20) frames 3DS flashcart

Loading before entering Garden of Madness
AANXAAN – 6(12) frames DS emu
Romscout – 8(16) frames DS
Diagon – 8(16) frames 3DS flashcart
Strizer – 9(18) frames 3DS flashcart

Loading before entering The Dark Chapel
AANXAAN – 6(12) frames DS emu
Romscout – 9(18) frames DS
Diagon – 9(18) frames 3DS flashcart
Strizer – 9(18) frames 3DS flashcart

Loading before entering Condemned Tower
AANXAAN – 6(12) frames DS emu
Romscout – 8(16) frames DS
Diagon – 9(18) frames 3DS flashcart
Strizer – 9(18) frames 3DS flashcart

Loading before cutscene with Julius in Condemned Tower
AANXAAN – 3(6) frames DS emu
Romscout – 4(8) frames DS
Diagon – 4(8) frames 3DS flashcart
Strizer – 4(8) frames 3DS flashcart

Loading after softresetring before doing boss rush up to the frame where “Licensed by Nintendo” screen starts appearing
AANXAAN – 11(22) frames DS emu
Romscout – 16(32) frames DS
Diagon – 17(34) frames 3DS flashcart
Strizer – 19(38) frames 3DS flashcart

Loading before entering Menace Fight (full white screen time)
AANXAAN – 10(20) frames DS emu
Romscout – 11(22) frames DS
Diagon – 12(24) frames 3DS flashcart
Strizer – 13(26) frames 3DS flashcart
As you can see, flashcart NEVER loads faster but rather slower half of the times. Also sometimes it has lag spikes which cost around 2 seconds (may both not happen or happen few times during the run). If you really want to differentiate 3DS flashcart runs with GBA slot I suggest adding third option for GBA slot - emulated GBA. That makes much more sense than marking console as emulated while it is not.

I appreciate Daigon doing the legwork & think the idea of an emulated GBA slot option opposed to making the whole run emulated is a good middle ground. In all of the above cases the flash cart ties or loses out to an actual DS, and always loses out to DS emulator so it doesn't feel fair to denote the 3DS played on actual hardware as emulator in that way.

Can also confirm lag spikes happen on my R4 cart. Typically during phase 1 of Menace when he uses his purple breathe attack. I've actually started delaying my next jump in that case cause it was getting into the habit of eating my jump input.

I do not own an R4 cart and have already put many hundreds of dollars into speedrunning this game so I'm sorry that I wasn't able to do accurate research. With this new information I'm open to adding an "emulated GBA slot" as a variable