The printer should work mostly fine with most distros, especially if they are based on Ubuntu repositories.
As @ptf has mentioned, not sure about the USB2HDMI switch for 2nd monitor output, might be worth trawling the Linux forums to see if anyone has encountered problems with a similar setup, as dual monitor output from a laptop (via USB no less) is probably not the most common of setups for the majority of Linux users.
Bluetooth audio seems to work pretty well in my limited experience, I have a Sony speaker that I can connect to the PC at home over Bt and it works, that’s good enough for me.
One issue you might find annoying, if you are a gamer, and you use a Bt wireless headset with built-in microphone. It appears that a combination of PulseAudio (the audio server daemon) and various Bt stacks provided by different Linux OSes do not always play well together, especially when it comes to automatic profile switching between A2DP and HSP/HFP. As I understand it (and I’m a total newb in this area) A2DP is the remote audio communication profile that allows a Bt headphone to receive audio data over Bt, whereas the HFP/HSP profiles are used for microphone pickup and transmission as used in telephony. I guess the only way to find out whether your particular headset works, if it is a wireless headset, would be to try and search through the forums beforehand.
As far as distros are concerned, my personal take:
Ubuntu has definitely become a staple - although I use it on several different machines, it comes with a number of pet hates - I upgraded to LTS 20.04 from 18.04 recently on 3 different machines, 2 of which were Dell laptops with an Ubuntu OEM setup. Those upgrades actually went fairly smoothly. The third upgrade on an older compact box is still giving me problems, but that is due to the Linux kernel no longer correctly supporting the BIOS of the motherboard. I had similar issues prior to upgrading, they’ve just got worse with the current iteration of Ubuntu OS.
I use ElementaryOS 5 on another older laptop, I love it for the simplicity of its UI, and its snappiness, but that comes at a cost in the choice of supported/integrated software. Although Elementary bases its repositories on Ubuntu, some software packages regularly found in Ubuntu are not present or are deemed “unsupported” (whatever that means exactly, as there is no paid support for Elementary as far as I can tell) and the developers for ElementaryOS have created their own app store and promote development of apps using the GTK/Vala environment. Upgrading from one version to another in ElementaryOS is still a PITA (unless suddenly, with the release of 5.1, they’ve made it easy).
I gave Manjaro a spin a few years ago, but it just didn’t appeal to me, probably didn’t give it long enough, I guess. I love the idea of rolling distros, but was always concerned about overall stability.
I haven’t tested Zorin in an age, it was still very young as a project when I last tried it, so that was several years ago !
For me Mint remains a solid Linux OS. Based on the Ubuntu repositories, and although now refusing to follow the snap package system provided by Ubuntu, it is one of those Linux distros that lets you get things done without hue or cry (mostly - I’ve had issues in the past too). Whilst I love the crispness of the Cinnamon desktop, I find it has become quite resource hungry (as is Ubuntu, to be fair) and I want my computer to boot up within seconds and be fully functional. Perhaps most of my hardware is now too old for that hope to be a reality.
Overall, probably what I regret the most about current Linux distribution development has been the trend to forget being economical with hardware resources, and instead go for the bloat or feature creep that we have seen in the commercial OS development. This is what attracted me to the Raspberry Pi. What the developers of that product have managed to do with those Arm processors is pretty amazing, and kind of puts the other mainstream chip manufacturers to shame, IMO.