My experience, it would only copy over ONE eSim:
I had 3 eSim on my iPhone 13 and it would only allow me to transfer one during setup. I had T-Mobile*, Mint, and US-Mobile. When it showed my eSims and asked if I would like to move any, I could put a check mark next to either T-Mobile or US-Mobile, but not both. Mint was greyed out and I wasn't allowed to transfer it in the setup. I chose to move T-Mobile, since that is my primary number.
*I had previously converted my T-Mobile physical SIM over to an eSim earlier in the week on my old phone.
Afterwards, I went into the Mint app and you choose 'Change Device' and you get a new eSim assigned to your new phone in a few minutes. Very easy, actually (although they sneakily re-enabled autopay when I did this).
I didn't bother figuring out how to get the US Mobile eSim back onto my new phone since it was for their 10 day trial and I don't plan to continue using them.
Now that more MVNO support eSim, I plan to switch my Mint plan over to a Verizon backed one - so I have double coverage. I use my second line as my business line, so I can slide it to off after hours.