I have a magento 2.4.3 running on a production server. I have the following error message in the admin panel.

Also some of the indexers shows "reindex required". I do not have the SSH access so how can I fix it from the admin panel?

I have a magento 2.4.3 running on a production server. I have the following error message in the admin panel.

Also some of the indexers shows "reindex required". I do not have the SSH access so how can I fix it from the admin panel?

There are two option for the indexer.
Update on Save : Update on save (realtime), Indexed data is updated as soon as a change is made in the Admin. (For example, the category products index is reindex after products are added to a category in the Admin.) This is the default.
Update on Schedule :The index is set to update on schedule according to a cron job, It is a preferred option. If you have larger database then it is recommended setting your indexers to Update on Schedule.
You can set cron job via Cpanel or SSH for the indexer.
I suggest you indexer set "Update on Schedule" and add cron jobs.