Is there a more updated, financially comparable iPhone to iPhone SE (3rd generation)?

That phone will get iOS 26 when it's released this fall. Aside from the features that will require Apple Intelligence, you won't be missing much of anything.

If you feel like you might want something newer, hold on until after new devices are announced this fall. When that happens, the current non-pro models are usually retained in the lineup with a price drop.

Your iPhone SE (3rd generation) will be compatible with iOS 26 (the successor to iOS 18) when it comes out in the fall. However, if you want to run Apple Intelligence, you will need to limit yourself to the discontinued iPhone 15 Pro and Pro Max, or to any of the iPhone 16-series phones.

The least expensive phone in Apple's new lineup is the iPhone 16e.

Apple – Compare iPhone models – 15 vs. 16e vs. 16

The iPhone 16e has Apple Intelligence, but lacks a few features like

• A Ultra-Wide (0.5x) camera
• MagSafe charging (it can do Qi wireless charging, but there's no magnetic help with alignment)
• Support for a wired connection to TV or monitor
• An Ultra-Wideband radio to support Precision Finding of AirTags

If the online Apple Store where you live has a Certified Refurbished section, you may want to take a look there. All Certified Refurbished iPhones come with a new battery, new outer shell, and 1-year warranty. So quality would not be a concern, but you'd still want to weigh the question of value. (Apple usually offers a discount of about 15% off original list price, and for an older model, that might not outweigh having fewer features, and very likely fewer years of future iOS updates.)

Refurbished iPhone Deals - Apple

Keep in mind that there are some features the SE has that the 16e does not and vice versa.

Is there something wrong with your SE3? The only thing it's really lacking feature wise is Apple Intelligence.

The iPhone 16e is the de facto “successor” to the SE (3rd Gen).

https://www.apple.com/iphone-16e/