Sorry for late reply TC. With a budget of $550+$200, you most definitely can get a better deal than that HP. For your use case, I'd suggest a used ThinkPad or a cheap gaming laptop from Best Buy Open Box.
Regarding gaming laptop, you obviously don't need its dGPU but its cooling should be able to sustain the CPU performance in turbo freq and protect your SSD from unwanted heat.
1.) ThinkPad A new one costs a leg so we'll aim for a used one. Various companies buy them in bulk then sell them after the warranty runs out, usually after 3/4 years. These ex-companies ThinkPads usually come in a (very) good condition without ugly damage or excessive wear and tear that people associate with used goods.
You should be able to get a 2018 model with 8th gen Intel or maybe even a 2019 one with 10th gen Intel / Ryzen 3000. See the T480 for starter, I once saw this for under $500. See also the slim X series and if lucky, the powerful P series with Xeon. Internet has a further buying guide for used ThinkPad.
With them you'll get a much better experience: - Cheap yet sturdy, durable and repairable - Pleasant IPS screen - Comfortable keyboard for long coding session - Great community support, modding, linux, and so on
The keyboard cannot be overstated, trust me on this. You won't go back to those usual keyboards on the $500 laptops after this lol.
Btw ThinkPad spec varies by regions, for example some may come with entry level MX dGPU. See the official site for details: https://psref.lenovo.com/
Beside Lenovo, Dell and HP also offer similar business line laptops. Iirc the keyboards on Dell/HP utilize half height keys for up and down arrow in a single line formation while ThinkPad has full sized keys in an inverted-T formation. I prefer ThinkPad for those.
2.) Best Buy Open Box Since you mostly have CPU-bound tasks, it's safe to assume the CPU will hit turbo freq constantly. This generates a lot of heat and if your SSD is exposed, you might risk a data loss.
SSD is usually rated for 60-70C at max. Please take this into account if you live somewhere hot and use a laptop with paltry cooling or high end proc. Look at a teardown video and use the farthest-from-CPU SSD slot. Throttle your CPU if necessary and use cooling mod.
Due to the heating problem above, a cheap gaming laptop from Best Buy Open Box actually suits your need. Get a cheap one from Asus/Acer. For school/office Legion laptop has plain old design without gaming aesthetic, might be out of your budget though.
Take for example the cheap Asus TUF F series gaming laptops. Their cooling often struggle to handle both the CPU and the dGPU at the same time however you won't engage the dGPU so no problem there. Plus better built, screen and keyboard than that HP.