My main domain is 25+ years old and has a great reputation, never used for spam or anything like that. I've been having the emails forwarded through WHM / cPanel to my Gmail.

7 days ago I moved my main site to a new VPS, and copied over the forwarders. But today I discovered that I'm missing the wide majority of my emails! I found them in WHM > View Relayers, about 241 out of 250 were rejected by my Gmail with this error:

TLS_AES_256_GCM_SHA384:256 CV=yes : SMTP error from remote mail server after end of data: 550-5.7.1 [<new VPS IP> 19] Gmail has detected that this message is likely\n 550-5.7.1 suspicious due to the very low reputation of the sending domain. To\n 550-5.7.1 best protect our users from spam, the message has been blocked. For\n 550-5.7.1 more information, go to\n 550 5.7.1 https://support.google.com/mail/answer/188131 af79cd13be357-93917765ba8si962882385a.175 - gsmtp 

I double checked in Postmaster Tools, and the domain's reputation is stellar. So when it says "low reputation of the sending domain", I have to assume it means the IP of the new VPS. MXToolbox confirms that the IP isn't on any blacklists, although the parent ASN is on the UCEPROTECT-Level3 list (which covers thousands of domains so it's not MY domain, but I can pay an extortion fee to get mine whitelisted).

Any suggestions?

I run a small hosting company, and have little to no experience with Wordpress myself. It's just something I offer clients.

I have one client that had a WP site built on a custom theme, using WP version 4.7.29. They also have these plugins:

Advanced Custom Fields 4.4.5
Contact Form 7 3.8.1
Document Gallery 2.3.7
Google Analytics for WordPress 4.3.5
NextScripts: Social Networks Auto-Poster 3.7.15
SSL Insecure Content Fixer 2.5.0
WP Realtime Sitemap 1.5.4
WordPress Importer 0.6.1

I'm removing the server that they're on, so I need to move them to a new one with PHP 8.4. I'm assuming that I'll have to install WP 7.0.2, too.

I CAN pay a monthly fee to install PHP 7.4 again, but is there a way to install the old WP version, too?

If not, any guesses on whether the old site will work properly with the updated software? How can I know other than "try it and see" (and risk breaking everything)?