if everyone raises rents by a certain percentage trying to recoup taxes, this will be equivalent of Supply line shifting up by the amount of tax in Economics 101 terms.

From economics we know that increase in cost is split between Landlords/Renters in accordance to their elasticities. Whoever is more elastic - will eat the tax.

the cost increase is shared between renters/landlords in the ratio of their elasticities. Whoever is more inelastic, will eat the cost.

Inealstic renters will pay up increased rent (like techbros in SF are eating up all rent increases).

Elastic renters will get up and move to Texas, if renter swill hike rent.

Elastic landlords will lever down and decrease number of low margin properties like rent-controlled properties, or unprofitable properties.

Inelastic landlords will eat the taxes and take a hit to profitability.