Spironolactone does many things and in some, even at high doses, does not reduce testosterone synthesis/production, but blocks all androgens including the stronger DHT to a certain extent and this would account for why men taking this drug and not seeing any reduction in T still experience gynecomastia, semen abnormalities, etc. The reason you are seeing an increase could be because spironolactone blocks androgen receptors and by doing so, your pituitary gland and hypothalamus aren't getting any negative feedback from the androgens circulating in your blood so that it thinks your body is not producing enough hormones SO it increases its signals, LH and FSH and up goes your T!
BUT, from my own readings, it seems that on spironolactone, T levels fluctuate quite a bit from day to day, up one day, down another so that they don't appear to be very reliable. The important thing though, IMO, is actual physical results and how you feel. If those are good, then you know that what you are taking is working!

Regardless of those numbers. A test can't measure how much is blocked, remember that and even recently, in a paper published in 2018, they admitted that measuring T levels on Spiro while treating transwomen is somewhat unreliable.
SHBG is increased by estrogen and will continue to be higher relative to pre-HRT because of the increased estrogen. This will bind more T, leaving less T available to bind receptors.
Finally, do realize that those numbers can be vastly different from one moment to another so another reason they can't be really fully trusted. Had you drawn your blood earlier or later, your T might have been low, E higher, etc.
Best of luck and keep us posted.