Some powered devices need to negotiate PoE with LLDP. Maybe you can try to enable LLDP on switch.

T2600G-28MPS and UAP-AC-LR both use mode A. Maybe they are 12(+)/36(-) or 12(-)/36(+). Generally the circuit design can make them be able to work with both polarities. But now they cannot work, maybe they only support one type of polarities and their polarities are different, or their PoE function already fail.

LLDP won't do the trick. The WAP has to be booted up, i.e. powered up, to entertain LLDP traffic. I tried it anyway, but of course it had no effect.

I've since got a PoE tester and the switch tests out 100% fine. The tester reports 802.3af Mode A T568B with the correct voltage, just like the switch data sheet says.

My current assessment is that Ubiquiti is lying through their teeth when they say that certain WAPs, including the ones I have, are 802.3af compliant. I am waiting on a second response from Ubiquiti to a trouble ticket I have submitted to them. The first response was "Oh, that WAP is 24V passive only." I then pointed them to both the data sheet and their own knowledge base article on PoE compatibility, both of which claim the WAP in question is 802.3af Mode A compliant.

@aa777888 I know this is an old post, however, I ran into the same exact problem around the same time you posted this inquiry.  I agree that Unifi APs do not seem to be compliant.  I have had an AP-AC-Lite for years that I tried to get working with my TP-Link TL-SG3424P after finally deciding that I wanted to go full PoE and start wiring up the house finally.  I found that neight my AP-AC-Lite, nor my Cloud Key Gen 2 would power up using anything but the unifi switch that I eventually purchased.  I just left the AP-AC-Lite on the passive injector bt did have to use the Unifi 16 port PoE switch to power the Gen 2 Key.  I never thought of testing this until now, but about five or six years back I had replaced two old Engenius Access Points with the single AP-AC-Lite.  I assumed the same thing you did by reading how the TP-Link switch may be inversely wired, based on some verbiage in their documentation.  However, I just decided to plug in my old EAP150 to see if it would power up on this switch since I am going to use it for some cameras that are coming.  Sure enough, after a few extra seconds of boot time, I am seeing all blue lights on the Engenius EAP150.  

@marteswigg Ubiquiti is lying through their teeth with their datasheets. Total BS. I had to buy a 24V passive capable switch to run the WAPs. No other solution. Period. Dot.