Boot up very slow on my iMac after macOS Ventura update.

The configuration looks fine, though something is causing I/O problems, and one possibility is a failing hard disk.

Run Apple Diagnostics (which can miss transient issues) or get DriveDx and check your storage.

The photo analysis tooling is also fairly busy, though whether that’s ongoing or transient, or a cause or a symptom?

Vinnie Delany wrote:

The slowdown only happened when upgraded to 13.6.5

Please download and run (free) EtreCheck, and share the generated report to the clipboard. Then open a new reply here, and select the Additional Text button that looks like a printed page to get a text input box big enough to paste and post the hardware configuration report here, and paste and post that.

This could be the usual slow iMac problem, or could be failing hardware, or could be some other issue or app.

That looks fine. Your Fusion hard drive is running exceptionally well. I see a lot of iMacs with problems via EtreCheck but you computer is running great.

The most likely explanation are those background photo indexing tasks that run whenever you do an operating system update. Since Apple releases those updates very frequently, it can seem like the system is always running slowly because by the time the indexing finally completes, there is another OS update and the whole process starts over again.

And if the only symptom you have is a slow boot-up, with normal operation running normally, then you are definitely running better than many people.

Vinnie Delany wrote:

Processor 3.4 GHz Quad-Core Intel Core i5 Graphics Radeon Pro 560 4 GB Memory 32 GB 2400 MHz DDR4

All of that is totally irrelevant.

iMac 21.5″ 4K

Now that's what matters. Those old iMacs typically have "Fusion" drives that consist of a small SSD with a mechanical hard drive. Sometimes they only have mechanical hard drives. You'll need a new computer.