Are new HDD now faster then?
yes
the old days started with 2.5-inch drives because that is what most people had in their systems and SSD just replaced that spinning rust... if you open one of those 1st drives they are mostly spare space
then we moved to M2 [which looks like Ram sticks] and that allowed laptops to be redesigned but was really the phone | tablet market which pushed the makers down this path
the current standard is NVMe which needed special boards to be bootable and blurs the line between Harddrive and Ram {one was storage and the other fast access}... the next generation of Ram will blur this line more
to get back on topic; your laptop is old and parts for it are no longer...