I was associate program director for a few years and reviewed a ton of ERAS applications. Date of birth appears on one part of the application, but quite honestly, I doubt most people even look at that. Probably the most commonly used filter is USMLE score (you can set for scores >220, etc) and then get a list of candidates that fall within your criteria.
I can appreciate your concerns as I was a "nontraditional" applicant for colorectal fellowship- applied after having been in practice for a few years. Though my situation is a bit different, I don't think it was too much of a hinderance, though I can appreciate why a program may be apprehensive about trying to train an older person who may be "set in their ways." On the interview trail, I thought it would be obvious but realistically most late 20 to early 30-year olds don't look drastically different than those in their mid to late 30's.
My guess is it may not be that obvious just by looking at you that you're roughly 10 years older than the "traditional" applicant though they may put 2&2 together by reading what you've done with your life thus far. I don't think mid-30's would be seen by most as a big deal (50 would be another story.)
As an aside, at the program where I was faculty there was a female resident (also a DO) who was a few years older than I was when I joined the staff. She was excellent, did very well in the program, and ultimately went on to fellowship. Until one day when she and I were talking in the OR, I wouldn't have guessed that she was older based on her appearance. I think having life experience served her well- she was very mature and respectful; one of my favorites to work with.
Good luck