Additional SQL Server features and topics not covered by specific categories
There are two ways to run the upgrade: in-place and move to new hardware. Since you are moving from SQL 2012 to SQL 2022, in-place upgrade can be difficult. It is not that SQL Server does not support it, but I don't think there is any version of Windows Server that supports both.
If you nevertheless do an in-place upgrade, the jobs are not an issue, they will keep moving along. If you move to new hardware, you can easily script them from SSMS and then use that script on SQL 2022.
No matter which path you take, I advice that once you have performed the upgrade, you enable Query Store on the database. Keep the database in compatibility mode 110 for a week or two. Then you can flip the switch to 160 to get access to the most recent optimizer improvements. Unfortunately, while they are improvements, they can back-fire and one or two queries may start to perform badly. With help of Query Store you can quick resolve the urgent situation by forcing the old plan, and then you can investigate the case for a more long-term solution later on.