I note you've already reset the SMC, but there are a few other things you can try as well.
Reset the NVRAM
To reset the Non-Volatile Random-Access Memory (NVRAM) on your model of MBP, follow these steps:
- Shut down your MBP (i.e. a full shut down, not just logging out).
- Press the power button and then press the commandoptionpr keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
- Hold those keys down until your MBP reboots again (i.e. a 2nd time) and you here the startup chime.
- Let go of the keys and let your MBP reboot normally.
Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).
If you find this makes no difference, you can also test to see what happens when booted into Safe Mode.
Boot into Safe Mode
Follow these steps to boot your MBP into Safe Mode:
- Fully shut down your MBP
- Restart your MBP
- Immediately press the Shift key and keep it down
- Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
- Take a note of what happens (i.e. try connecting your display to determine if the issue is still present, etc)
- Exit Safe Mode by restarting your Mac normally and try connecting your display again
If your display connects during Safe Mode but doesn't connect afterwards when booted normally, let me know. Otherwise, if you had no joy regardless of whether you were in Safe Mode or not, it's probably time to test your hardware.
Run Apple Hardware Test
Your model MBP uses Apple Hardware Test. To use this, follow these steps:
- Shut down your MBP
- Restart your MBP
- Press and hold the D key before the gray startup screen appears.
- After a while, Apple Hardware Test (AHT) will start.
- When prompted, select your language and click the right arrow.
- When the AHT console appears, you can choose to run Basic tests by clicking the Test button. However, I suggest you select the "Perform extended testing" checkbox before you click the Test button.
- Your test results will appear in the window in the bottom-right of the console.
Note 1: that the extended test will take some time. Take a note of the results and report back.
Note 2: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete.