So I've had my 2015 Macbook Pro for about 7 years now. The trackpad has been (occasionally) behaving erratically for the...

Your MacBook model suggests it supports True Tone. All displays with True Tone support are paired to the logic board and swapping them will disable the feature entirely.

Unfortunately, all Touch ID sensors are paired to the motherboard on all Apple devices. Replacing either will disable the fingerprint reading functionality.

Since you don't hear the drive even "try" to eject, the problem could simply be the front panel of the case. That big eject button in the images simply pushes on the drive's built-in button when pressed. This "soft clicking" sound you describe may indicate that the button is broken. You should remove the drive from its caddy and try to eject the disk by pressing on the actual button of the drive unit, which is most likely still fine. If you can't remove it from inside the case, you should be able to remove the front panel of the case. There is usually a large gap at the bottom, large enough to grab firmly and pull out (might require some force).

The cause of the problem was the accumulation of grime and debris underneath the trackpad after many years of use. I cleaned the perimeter of the trackpad with a cotton swab, some alcohol and compressed air, being particularly careful around the thin ribbon cables connecting the glass surface to the logic board. At the time of writing it's been 7 months since the cleaning and the problem is completely fixed.