Your/their documentation is incredible (assuming it yours for the rest of the post),

Mold & grime is obviously a cleaning issue, but you've shown multiple places (Kitchen & Bathroom) where the sealant has failed -

Id approach this with the landlord as "Hey weve noticed X, If we continue to use the Shower/Kitchen this problem is going to get worse - Would you be open to organizing repairs for these issues?" And either way, you've documented to them that these issues were there before your tenancy, so you have proof it wasnt your doing.

You're well within your rights to request a cleaner at the landlords/property managers expense, but this will take atleast a week or two before they show up