Not sure of your impressions of Battle Stage, kind of feel you might not be a fan of them. Did you check out Battle Stage 3, apparently the original version of it was a very low effort part on the production team since they literally cut up the races and had no dialogue - an Initial D fan modified them to include dialogue that was missing and shared them on RU-vid. Battle Digest is kind of low effort as well since it just cuts up the races, but at least they reintroduce a SEB soundtrack which makes up for it. I do get the feeling that like what seems to be a common theme with Initial D fans is that Fifth/Final Stage is not that good. The only decent parts were the R32 vs FC race (although the backstory was trash) and the final 2 races - still wish Shigeno and the team that did the anime at least gave us a pay off with a Keisuke vs Takumi rematch. There was so much room to do something interesting in the Project D arc, besides a eisuke vs Takumi rematch, they could have done something interesting like have either Keisuke or Takumi lose a race in Project D (although I guess it could be argued that Takumi lost the last race), would have been more interesting to see the fallout of something like that - perhaps Keisuke taking on the opponent on the downhill. Even some of the races could have been done differently like having the MR-S vs 86 match be more even, another Initial D fan made their own version which was 100x better. The other thing is the FD vs Z race was awful, Shigeno could have used something better than something that could be viewed as cheating to win (although despite knowing there are no oncoming cars, it still takes some guts to overcome natural instincts when driving through fog). Thinking about this makes me wish that they had pivoted a little more to Keisuke in Fourth Stage onwards to show his progress since First through Third Stage were showing the progress of Takumi.
I'm a fan of battle stage 1 but not 2 and 3. I also wasn't a fan of anything after stage 3. Not into the God arm and God foot thing. Project D was designed for casual watching's of more Initial D content. Sometimes shows should just ended while they are on top and leave people wanting more and not making anything else. I don't think the other stages tainted the legacy, but I don't think they should have been created either.