Use the laptop microphone as the input instead, or if no microphone is present just buy an external microphone. You probably don't need a $300 podcast-class microphone since the audio still gets compressed in transit, though.
A decent mic will still outperform.
For the love of everything, use something standalone. Ideally not a desk mic. Vibration works against those... just like what's built into any given laptop. It's a form-factor/usability thing.
Decent audio isn't a price problem, it's entirely about selection. What you suggest is my last choice. A backup.
Headsets and forgive me, wires I can replace, are hard to beat. I like to type, talk, and be heard. Sometimes all at once.
The degree to which vibration of is a problem depends on your setup. If your laptop is mounted on a VESA arm bolted to your desk and you’re typing on an external keyboard for example, it’s not going to come through too easily, especially if you have the keyboard placed on a desk pad. This is true of a standalone mic on an arm too.
Misunderstands the value of a good mic. That's like saying DSLRs and flip phones take the same quality photos if you are compressing them down to 400x400 JPEGs
You'd be surprised at how many companies/etc issue laptops that don't handle background noise for anything, even the fan on the laptop itself.
That said I've been using one or two variants of a gaming headset with dedicated receiver for the last 5-ish years. (Before that I used Logitech H800s with the dedicated receiver, alas the earpieces disintegrated after a decade or so.) Better audio quality and at the time were only 100$ on sale.
Especially if you are in an open office or pit style setting, bluetooth just has too many issues to be reliable/good for wireless audio.
It's honestly a pet peeve of mine when people consistently lack audio etiquette. Communication is a huge part of our job, remote work is a godsend for work-life balance, it should be the bare minimum to just mute yourself when you're not talking and in general being mindful how much sound interruptions you're repeatedly causing in group meetings.