You can use WordPress's Custom HTML blocks feature to collect subscribers for your Buttondown newsletter, all without needing to install any additional plugins.
First, create a new Custom HTML block. To learn more, read WordPress's documentation.

In the Custom HTML block, paste in the following code:
That's it! The new Custom HTML block will display a subscription form for your Buttondown newsletter.
Warning
If you edit the pasted markup, take care to keep the name="email" attribute intact — if it changes, submissions will silently stop reaching Buttondown. (This is the failure mode the official plugin exists to prevent.)