So I have a website where I post affiliate product reviews etc. Let's say it's example.com. On this site, I post international product reviews which have worldwide shipping. Recently I bought example.in and I am planning to put only product reviews that ship to India only as .in is for India. Also, I will select the target country in the search console as India for this website. Now my question is since both these domains have a common name example, will they affect each other's SEO?
The answer is definitely Yes. Considering you are using same reviews and the only difference would be that the later has products that only ship to India.
It will help if you make sure that shipping destination becomes a value proposition on each website and why not, since content will be very similar and the reviews belong to you, go ahead and make a reference to each other using hreflang (only if websites are in different languages).
If they are not in different languages, alternatively you could create excerpt of each review or present the full review. On any case always link from xyz.in to xyz.com to refer to the original review, this is a technique similar to content syndication.
Note that Google wants to rank the original content first – even if it doesn’t always happen. Read about google guidelines on duplicate content here