What I believe you can't do is have your own frontend send the data in the form to your own backend, then forward on to the other service from there. Once the plaintext card details touch your servers you have to be PCI compliant, even if you aren't storing them.
If you absolutely can't do the former on your frontend, eg because you don't want to use JS or something similar, then you can use services like Stripe checkout where they host the frontend on a URL you redirect to from your app, etc.
In general I am a fan of just using things like Stripe Checkout though - it's not just about compliance but also just the complexity of getting the frontend part right with the myriad different payment flows, errors, and other subtle details that exist.
But my original comment was more just clearing up confusion that you can absolutely do the frontend UI customly if you want to - there's no issue with this and PCI compliance, that only kicks in once the data goes to your server.
Have you considered using Stripe Elements? It has loads of customization options that you can configure using an appearance API
It seems like a veil of security versus any actual security. My guess is that it's really just meant to assign liability to the merchant when nefarious stuff happens and there's plenty of ways a fraudster could shield themselves from that as well.
At the end of the day, as a customer visiting some random merchant website showing a "Powered by Stripe" logo does not actually make me feel like my CC data is secure. Anytime I enter info into a UI/DOM that is not directly under the stripe.com/paypal.com/etc (full page load), I don't feel my info is necessarily safe; but that's what they want me to believe. It's totally possible to just put a "powered by Stripe" UI element on a page without having any relationship with Stripe. And, the false security of that UI element tricks you into putting your info into some random site. I just don't see how that's secure at all to train users that anytime you see that UI element you can safely input your payment information regardless of the site you are on.
Stripe aside, if you claim to not be in scope, but that claim is in question, then you’ll likely have to prove you do not improperly handle card data to an auditor, or risk fines and/or loss of any funds you’ve accumulated so far.
PCI isn’t perfect, but they do have business reasons to stop most obvious bad behavior.