Sara M. classic - this really comes down to your personal preference - do you want easy access to get the codes and update them when necessary and always be tied to this client for as long as the website exists or do you want to go through the painful process of showing your client how to grab the code and maintain that code within Webflow? I say painful process because Google likes to make things more difficult.
Are you positioning yourself as somebody who is more hands-on, or somebody that does one-off projects and moves on?
Each have their pros and cons.
sometimes they need updating - its pretty rare - but fast-forwarding 5 years and 30 clients later, you've got recaptcha keys for 30 websites that you might have to maintain within your account infinitely.
if Webflow changes how they support it, v2 to v3, I can't even recall a time I've really had to update it - I might be getting it confused with how WordPress breaks literally everything.
but I also think recaptchas got a premium option for bots and then tied to a google wallet for payment - then it gets pretty messy if there's potential for charges.