My first suggestion is to “work offline” and try to delete.
Second, rename the PST file, move it to another folder and launch Outlook. Configure it again for your email, and test the delete option by moving a test email and then deleting. If it functions, then you can rebuild your inbox, contacts, etc by importing only those items back into Outlook.
Go ahead and assume your PST is corrupt and not salvagable. If possible, you should export important email through “file, export” to backup those messages before the PST becomes unusable.