What Dah•veed said.
This is Apple's explanation for using your Apple Watch with a 2nd SIM (or eSIM) on your iPhone
Use Dual SIM with Apple Watch GPS + Cellular models - Apple Support
Use Dual SIM iPhone with Apple Watch - Apple Support
There is no workaround to adding an Apple Watch to a Mint Mobile account for a prices similar to $10 U.S.
And if you were to get a 2nd phone number at Full Priced, and more expensive then Mint Mobile, then you might as well just switch your Mint Mobile phone number over to the more expensive cellular provider, and stop using Mint Mobile.
T-Mobile has some less expensive plans that do support the Apple Watch. Also some cable companies that also offer cellular also support the Apple Watch, such as Comcast/Xfinity and Spectrum cable (there may be others around the country), and these plans tend to be less expensive when bundled in with your cable services.
I realize it is possible you have Mint Mobile for reasons besides its low cost, but if cost is the only reason, and you are willing to pay for a second more expensive cellular plan in additional to Mint Mobile, it does not make sense to me.
Also, as a long time GPS only Apple Watch user, I always have my iPhone with me (I'm a guy with pockets, that does not care if it reunions the line of my clothes 😀). I have never missed having cellular on my Apple Watch.
My Wife on the other hand does not carry her iPhone in her pocket, and does own a cellular Apple Watch on a T-Mobile plan.
Limitations using a 2nd full priced cellular plan on your iPhone.
The Cellular Apple Watch is paired to your 2nd phone number, and shares the 2nd phone number.
When you are near your iPhone, both the 2nd and Mint numbers will ring on your Apple watch because the iPhone answers the calls, and uses Bluetooth to activate the Apple Watch speaker phone.
When you are away from your iPhone, ONLY the 2nd phone number will ring on your Apple Watch. Your Mint Mobile phone number will ring on your absent iPhone, and eventually go to voice mail.
If you use SMS/MMS TEXT messaging with Android phone users, or you have web site logins that send an SMS with a 2nd factor code to login, then ONLY SMS/MMS TEXT messages sent to your 2nd phone number will appear on your Apple Watch when you are away from your iPhone.
Those are the 2 biggest limitations to using a 2nd phone number and pairing that to your Apple Watch.
Most other services are Internet based, and the 2nd phone number provides vanilla Internet access which does not care about phone numbers, so your iMessage, email, calendar, Walkie-Talkie, FaceTime audio, weather, streaming music, etc... do not care what cellular carrier is carrying the data to you.
I'm understanding your post to mean that my unlocked eSIM is compatible with multiple cell service providers simultaneously, is this true?
The eSIM can be used with any carrier that will support an eSIM. It can be any carrier. Typically, it is used by business people that need a personal phone number and a business phone number, or by international travelers that want to get a local cellular service while out of the country because it is cheaper than the roaming chargers their cellular carrier will charge, and cheaper than the data chargers their carrier will charge when out of country.
But it has been used, mostly by users where the company owns the iPhone, to add a personal line which they can pair their Apple Watch. Again, the limitations mentioned above apply.
...could you expand on this too? If the watch’s service is prioritized, then I imagine that this would allow it to fully function when away from my iPhone - can I prioritize one number over the other instead of the cost making that determination?
The Apple Watch shares the phone number with the iPhone. This requires special support from the carrier. In some cases the carrier does not do this because it is not worth the effort by the carrier to implement this in their system.
Sometimes a carrier does not implement this because they are an MVNO, such as Mint Mobile and their contract with one of the Big 3 carriers in the U.S. does not allow them to offer Apple Watch support. To get Apple Watch support the MVNO would have to pay their Big 3 partner a lot more money and that would raise their inexpensive rates.
The above mentions Comcast/Xfinity and Spectrum are MVNO's that do pay their Big 3 partner extra for Apple Watch support.
So, no, you cannot change the priority of which phone line the Apple Watch pays attention to, when one of the lines does not directly support the Apple Watch.
My Wife is talking me for a walk. I have to end this here.