The Texas Medication Algorithm Project was corrupt from the beginning (unsurprisingly), with significant drug company funding. It was influential in other states for medicaid patients back in the day too. But it is flawed and not considered best practice these days. The Harvard/Southshore algorithms never caught on. In general guidelines in psychiatry have never been influential in the US for various political reasons. The APA (which produced and is again producing practice guidelines) did not want to upset membership by being too narrow or evidence-based in recommendations or creating a standard of care which would be used as a stick by malpractice attorneys to beat membership with and so the guidelines are pretty vague and useless and the old ones were (unsurprisingly) medication-heavy.
If you are looking for guidelines to inform practice, you need to look overseas. A good place to start is the British Maudsley Prescribing Guidelines. You can also look up the canadian
CANMAT guidelines (for bipolar, depression, anxiety), the British Association of Psychopharmacology Guidelines, the british
NICE guielines and the
world federation of societies for biological psychiatry guidelines. Obviously caveats apply as dosing of some drugs is different, some meds not available overseas and some not available in the US etc.
Psychiatry does not lend itself to algorithms as well as some other specialties (e.g. EM, medicine). That means there is a wide range of different practices including poor care, but it also reflects the nuance of psychiatry and the need for personalized care.