I have Family Tree Maker 2019 as well. The specific version when viewed in the menu bar at Family Tree Maker > About Family Tree Maker is reported as Version 2019 (24.2.2.560). I have no problem viewing the tree and it remains on the screen. I have tested it by leaving it open for the last 10 minutes.
You definitely want to make sure you backup your information by using the File menu. This won't overwrite any current information and will create a new data file. Make sure all options are checked so the backup file includes all of your media. I can't offer any additional information then what has been given to you by MacKiev, but can confirm the app works fine for me on Sequoia with no warning messages. I understand not wanting to lose 20 years of research.
If you do decide to remove and install Family Tree Maker again, they do provide this Support Article to restore from your backup. They also say there may be issues with AntiVirus software, so if you are using any, I would remove that and test Family Tree Maker again.
https://support.mackiev.com/487839-Restoring-from-a-Backup-in-FTM-2017-and-FTM-2019