It's a good idea. One larger site outperforms two small ones.
I think you should do it in one go. Copy all the content to the new site, and then do a full redirect of the old site URLs to the new site URLs, including the home page URL. This would be a signal to Google that the site has moved in its entirety.
You might also get a boost in link juice, as all the links that pointed to site 2 will now point to site 1.
Proper redirections are key. Every single URL must be redirected.
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