PowerBI Embedded sounds like what you want:
But make sure to check all of the products listed in the PowerBI service tiers. Also make sure you understand what it's going to cost and who is going to pay for it. Also double-check GuyInACube on each product tier. There's some feature comparisons on the pricing page if you scroll down:
FYI, PowerBI Report Server was just updated September 2022. It is intentionally less powerful that PowerBI Premium, but it offers you quite a few features:
The only major downside is the only non-Premium license allowed is SQL Server Enterprise with Software Assurance, so you won't save any money if you're not already licensed that way.
My personal advice, you almost certainly don't want your clients pulling reports from your PowerBI subscription. You'll have almost no way to control costs. And someone will very likely ask for a Premium-only feature, and those costs will explode. There is an option for premium per user:
But I'm not sure if you can change that after the subscription is created.
Might want to browse the PowerBi subreddit:
https://www.reddit.com/r/PowerBI/
I found some interesting posts when searching for "cost" and "embedded". Make sure to check the dates on things, apparently some cost estimates were based on old pricing models.
I mentioned some other things in an old thread:
The one point I'd carry from that one is how often you'll be refreshing your data, and if you can do it incrementally or not.