New Laptop or After effects?

You really want something that falls in the "mobile workstation" category, ideally with 32GB of RAM or more, 1TB SSD or larger, Intel 13th gen i7 or i9, and dedicated graphics (6GB or more).  

For what it's worth, any variation of the Apple Silicon-based 16-inch MacBook Pro is excellent for Premiere Pro, After Effects, Cinema 4D Lite, Photoshop, Illustrator, Media Encoder, Animate, InDesign, and Audition.

I'd expect good performance working with 720p ProRes 422 LT in Premiere Pro with HP ProBook 455 G7 with an AMD Ryzen 5 4500U with Radeon Graphics 2.38 GHz and 16 GB RAM, maybe 1080p, and to be very patient when it comes to rendering.

Like Peru Bob stated. It's your laptop. Specifically, the reliance entirely on the on-CPU integrated graphics that does not have its own discrete VRAM at all, but instead steals a ton of the system RAM for itself, substantially reducing the amount of RAM available for the operating system and programs. With such an extreme amount of system RAM that is usable only by the integrated graphics and nothing else, your laptop's available system RAM amount becomes woefully insufficient to run After Effects. In the worst cases, the integrated graphics steals as much as 10 GB of system RAM for itself, you would be left with less than 6 GB of total available system RAM to run the operating system and any installed software.

If it is slow in Premiere Pro, it will be slow in After Effects.

Part of your issue is the integrated and not dedicated graphics.

What are the hard drives (how many, what kind, what is on each, what capacity, and how full)?

Have you tried proxies?

https://helpx.adobe.com/premiere-pro/how-to/proxy-media.html