I'd be very surprised if this is an STI, and not something totally unrelated.
There are lots of reasons for mucus in your stool, but an STI isn't one of them.
https://www.healthline.com/health/mucus-in-stool
After 6 years, it would be really surprising if you had gonorrhea or chlamydia without any symptoms, and you've tested negative for HIV and syphilis. Herpes causes blisters, and HPV causes warts.
If the mucus continues, or is accompanied by pain, cramping or blood, you should see your doctor, but it's not related to an STI.
Not sure what you mean by mucous in your stool. But yes, some STDs can take a long time to do their damage. But not the symptom you describe.