Might using Bluetooth headsets to output audio damage them

There are three problems to overcome:

Signal-level mismatch and Impedance mismatch

The simplest way to pass audio signals between devices is to connect line-in to line-out. Your devices lack line-in and line-out ports, so this isn't possible.

The signal needed to drive headphones is larger than the signal produced by a microphone. You should expect a lot of noise and clipping. It might be feasible to use a potentiometer to attenuate the signal.

The usual solution is a Direct Injection Box but you could try a pair of Attenuating Dubbing Cords.

Stereo vs Mono

You also need to convert stereo headphone signals to a mono microphone signal. Use a stereo to mono adapter

Feedback Loop

By creating a signal loop, you run the risk of creating feedback (howl-around). Make sure the laptop outputs are not monitoring the microphone input.

By bluetooth... which profiles are you implying "works" and "doesn't work". Typically, if you're using "A2DP" for your audio output, your microphone won't work. A2DP requires a significant amount of bandwidth that will not allow for a "Hands Free" profile while transmitting audio. Most headsets (that I've used) require you to switch to a "hands free" profile that sounds like garbage (mono, low-quality, etc...) but will allow you to use the microphone. Sometimes, that "switch" must be done manually... by disabling the a2dp profile and enabling the hands-free profile. Windows sees the "output device" for a2dp and hands free separately... so if you have a program playing music... and you switch to hands free... the music will keep playing on the a2dp interface (going nowhere essentially) and your hands-free output device is the only thing that will work.