Domain Redirect Factors

When I purchase an expired domain to redirect it to my own domain for SEO purposes, what is considered to play a more significant role?

The Domain Authority of the expired domain, or the number of referring domains with backlinks?

To share my opinion, I believe that in such cases, backlinks are what provide the most value, regardless of the authority. Even if the results are very temporary.

However, I would like to hear other opinions as well...

None of them, you can get both good metrics & high RDs by spamming the hell out of some domain with tools like GSA SER,
You have to manually go through the link profile and check some/most of the links manually, the linking pages/domains, etc...

Keep such metrics for filtering your searches instead, ofc, not Moz DA, it's the worst to rely on, just use DR/RDs,
You can find plenty of spammy high DR/RDs domains, but you're less likely to find a good domain with low metrics (which could happen tho)

DA can be easily manipulated and inflated, it's not a reliable metric

backlinks and RD hold more value that doomain authority as they differently impact link equity and ranking potentials.

Just checking the domain metrics will not work, and most of them will be spammed. As advised by @hideath, you need to verify manually the linking domains, content, relevancy, anchors, traffic, niche, history, etc.

Keeping your domain redirects up to date is crucial to maintaining your search engine optimization, user experience, and brand consistency. The key factors to consider include selecting the appropriate redirect type (301 vs. 302), ensuring proper URL mapping, avoiding redirect chains, and monitoring for broken links. Having a well-designed redirect strategy will increase traffic to your site and maintain your search engine ranking.

From experience, one of the most reliable looks at a domain link profile trust metrics is combining DR with Majestics's Trust Flow and Citation Flow. A big difference between TF and CF should raise alarm bells