First, we (Managecast) are a Veeam Service Provider and 85% of our business is centered around Veeam so I suppose you could say I am biased - which is probably true. I'm also owner of the company and if there was something far superior I could change. We love Veeam. Our clients love Veeam.
As for your specifics Veeam checks almost all of your boxes and I have a few comments as well:
Immutability, check. You can roll your own with Veeam Linux Hardended Repository, or we also support hardened linux repos with immutability as part of our service as well as additional immutability using Zadara
Veeam, to my knowledge, does not support MFA - at least their core product: Veeam Backup and Replication. they do support it in other products like Veeam Service Provider Console. Of course you can add MFA to the Windows server running VBR, but the back end backup connections are not going to be MFA. Someone can correct me I am sure,
File, VM, BMR recovery - yes, of course. (will also let you do granular AD object recoveries, mail message level, etc)
Site-to-site replication (private cloud) - yep.
Cloud support - Yes, we provide offsite backup and DR replication. You can get support from Veeam, but we (Managecast) also have 4 Veeam Certified Engineers, won the 2020 Veeam Innovation award for our Veeam portal, and in general walk, talk, sleep Veeam. Our job is to make backup and DR as easy as possible for our clients which includes a high level of support. If we can't fix it we have Veeam engineers dedicated to our account, access to service provider support forums, etc.
IP Re-assignment for DR - We generally never re-ip customer networks in the DR environment. We virtualize the customer's private network behind a software firewall and maintain the original IP address space. We can even failover branch-offices and other networks into the DR environment. You could re-ip, but we choose not to for our clients and we've not had issues. Also be sure to know about Veeam Network Extension appliance. It is one of the most powerful, underused, tools out there and is a beautiful thing.
SQL Cluster Support - no problem.
MYSQL - Yes, supported, but really need to know your Linux version to see if it's compatible with Veeam Agent for Linux. Worst case you will need to backup the dump files.
Windows, Linux (be sure to check Linux flavor/version)- yes
Logging, alerts - yes, extensive. See the portal we created to track: (oh and portal supports MFA!)
Granular retention - retention is at the job level. You will need different jobs for different retention policies. Be sure to use Windows ReFS or Linux XFS if you need GFS retention. Otherwise storage will explode.
Granular templates? Honestly not sure on that one! I have not heard of it in Veeam. Maybe someone else can comment?
Scalability - yes, very large enterprise deployments into the petabytes
Vendor support - Veeam is a $1 billion dollar software company. Combined with Managecast's 22 years in business and our relentless focus on Veeam I am not sure how you could be better supported.