Quick Recap
Let's say you have two sites with two different domains for...coffee bean reviews, one is in German and the other in English. The images and text are similar but the main difference is obviously the language.
Google will treat these as stand-alone sites. Which is fine. My guess is that you know this, but others who find this might not.
Hreflang = Your Best Friend
For any/all (indexable) pages that have multiple language versions, I always recommend using the hreflang
annotation - and using it carefully.
Especially for multiple language/country combinations.
The same set of hreflang statements should be used on each language version of a page.
Typically, your canonical url, ex: <link rel="canonical" href="example.com" />
should be specific to each language version of the page.
The hreflang annotation, however, should always be the same on all equivalent versions of the page. This is true whether they're on the same domain example.com/fr
vs. example.com/es
or cross-domain.
There are many "true" ways to handle internationalization. In my experience, what you describe is a perfectly fine way to handle your situation - your instincts are good. Use that exact match domain!
As long as you set your hreflang
annotations and canonical urls properly, and I can't see how this would backfire on you.
Google ranks pages not websites.
Examples & Resources:
Example Hreflang implementation (via Google Developers)
Slightly modified formatting and info about x-default
<head>
<title>Widgets, Inc</title>
<link rel="alternate" hreflang="en-gb" href="http://en-gb.example.com/page.html" />
<link rel="alternate" hreflang="en-us" href="http://en-us.example.com/page.html" />
<link rel="alternate" hreflang="en" href="http://en.example.com/page.html" />
<link rel="alternate" hreflang="de" href="http://de.example.com/page.html" />
<!-- x-default is required -->
<link rel="alternate" hreflang="x-default" href="http://www.example.com/" />
</head>
Google's International Targeting report <-- Must Submit for All Properties
The hreflang Tags Generator Tool <-- Aleyda has tons of additional guides on hreflang and International SEO
https://app.hreflang.org/ <-- I occasionally use this tool to test complex implementations