Bike is 1999 Specialized Allez with 9 speed cassette and triple chain ring. The rear brifter (ST-5500) downshifting is jammed and probably not repairable. If I upgrade to Ultegra, which models work?

I tried to search and found differing opinions on whether 9x2 brifters will work with triple rings for front brifter. Are there different models within the ST-6500 series that differentiate double and triple rings? ST-6500 series are the only Ultegra for 9 speed?

Any recommendations on microShift of any others?