There are some checklists out there on blogs and such but there is no one size fits all. Every environment is different. I've had different upgrade processes when working at the same company. You need to ask for specifics on how and what different pieces are used such as asking what the different packages do. Those are more complex due to some of the dependencies. Where to get information on the packages depend on how they use SSIS in terms of storage - on disk, in msdb, ssisdb, etc. If they have any developers or source control, you can probably access rdl and dtsx files as well as various SSAS files (database, cube, ds). Those will give you some information in XML.
But you will be the one coming up with questions to ask - do you know how they store or execute packages now? What do they do with maintenance? How do they manage access control? Some ideas around checklists and links to those:
The Migration Checklist
SQL Server Migration Plan
SQL Server Database Migration Checklist

There are quite a few like that if you search on SQL Server migration checklist.
Any action item is something you need to know about so just start asking them questions related to that. For example, all the checklists will mention backups so you would want to know how they do those for all of those components - do they schedule them, do they use SQL jobs, do they use third party products, where are things backed up to, etc. So the migration checklists would drive the questions you ask them.

Sue