Why do I have persistent BO despite taking care of myself?

I might get a complete medical exam and ask your doctor about it to rule out an infection. Get dental checkup too. Dental problems can cause an odor.

Also, do you eat a lot of garlic?

I have an allergy to deodorant. A Mayo Doctor told me years ago to use.
5 parts water
1 part white vinger.
Do that for a few days then back off. You can do this many times. It works for me.
Also. You should make appointment with your doctor. If they are at a lost. Go to an allergy doctor.
I do understand what you are saying. After a fall I went to rehab for 2 weeks. You want to talk about smell. It took me 2 weeks to get the smell off of me. The rehab and the hospital I had a total of 3 showers in almost a month.
It was bad.
Wish you the best.

You didn't indicate your age. There is an old-people's smell. I've read that best thing for that is to eat mushrooms or supplements which has a chemical that blocks that smell.

You should have your thyroid checked for nodules or goiters in your neck (ultrasound/ sonogram) see an endocrinologist & also have a cbc with differential blood work . Stop using baby powder and perfumes with high alcohol content . Use non fragrance creams & lotions in private areas . Try using All or fragrance free & clear dermatologist approved laundry detergent. Eat cinnamon as it cuts sugar & helps you smell better. Try eating blueberries 🫐, fresh fish& vegetables ( never frozen or canned) wash hair with real strawberries 🍓 using a gentle shampoo if hair is oily use listerine original ( not flavored) on your scalp on damp hair only then a gentle conditioner. Eat natural foods not processed this should help with sweat and foul odors

Great tip! I love gardening and work up a big sweat and never had an uncommon issue with BO until this year at age 76. Just washing with my allergy free soap didn't eliminate the odor even after showering. Your tip about vinegar works for me. I am allergic to several ingredient in most deodorants. Tom's fragrance free was the cleanest commercial deodorant product allergen free for me and it worked for years, but stopped about 6 months ago plus it would irritate my underarms if I used it more than every other day. Yes after gardening I'll still get BO but I discovered the benefits of vinegar. At the start of my shower I spray or splash a mixture of equal parts vinegar and water under my arms, wait a minute then rub in well with my lard and glycerin soap, like Grandma's (also allergy free for me). I wait to rinse off until the end of the shower. I do this daily. So far now after months of doing this no irritation. Apple Cider Vinegar was recommended. but I've also read that basic inexpensive White Vinegar also works.
Before, simply using soap wasn't enough to kill the odor totally.
As far a feminine odor which I also developed later in life when hormones were no longer prescribed I've got that solved. No issues anymore because of a vaginal ring with time released estrogen, Estring. Expensive, but so worth it to me. I can't use inserted estrogen creams or foams because of the inactive ingredient in this topical estrogen because in middle age I developed severe Allergic Contact Dermatitis, ACD. This ring, Estring, stays in for 3 months and has restored my natural secretions which clean out the vagina. If you don't have allergies to the inactive ingredients try the topical vaginal creams to save money.
Keep searching like Minnesota10 and I did.

My husband developed a sour-smelling body odor from his chest. Saw several specialists over the course of two years trying to determine the cause. Finally he was diagnosed with Parkinsons Disease. Unfortunately this is a real thing. Can also be musky/greasy smelling. Suggest you get tested.