I dig your idea, it will make people checking their game often.
Simple version of this also exists in Sonic at Olympic Games - Tokyo 2020 mobile game.
Used to play the game daily just because of this feature.
I've got ideas on how the "Avatar Battle Mode" could work. I've jotted down all my "fan game ideas" I've had for years. To sum it up if Avatar Battle Mode is a Sonic-copy of PSO2, I can imagine
the new Restoration HQ being like the ARKS ship for Avatars. Or the very least the town center of
Sunset Heights/
Park Avenue be made as the shopping district for Avatars. I can imagine a brand new Avatar customization with "
Speed,
Power, Fly and
Technique" serving as a class system for Avatars. Haven't decided if certain coloured wispons are limited to your Class-type or grants unique functions with them.
And like traditional Battle Mode from Shadow's game, Avatars can be pitted against one another in arenas, but I'd rather expand it to be like Team Fortress 2 with a variety of competitive modes to choose from.
Other than competitive matches there is also racing matches, with
virtual hedgehogs substituting Sonic.
Factions might be a thing. Players could probably make their Avatars join the
Sonic Resistance or the
Eggman Empire. Kinda like World of Warcraft with the Horde and the Alliance.
About adding new thing in PSO2, SEGA could also still feeling bitter about Phantasy Star Online Episode III: C.A.R.D. Revolution.
It has such a good idea for a spinoff but the general reception wasn't that good.
I never played PSOe3 but I've seen clips of it which looks like Sega were trying to copy the Yu-Gi-Oh craze at the time. I agree it did look good but it looked better off as a side-game than the need to be the main game.
Like
Triple Triad in FFVIII or
Tetra Master in FFIX.
They could of still give C.A.R.D. Revolution it's own story episode... just accessable in the Casino area while Episode III had a more proper story. (Did PSO1 had a Casino? I can't remember.)