Question Why get an ap instead of a router in ap mode?

I found many many recommended "good" routers for far cheaper than i found any access point, so are access point's wifi actually better, or are the routers (if put in ap mode) just a better deal?
The key feature you find on most AP is they can be powered by PoE. This is important when you say want to mount them on the ceiling and have no power. Most other AP feature are related to large business installations. They have feature that assist in setting power to get good coverage. Some have controller software that attempts to balance the user load between AP.

For your general home user a router running as a AP will be cheaper.....then again some routers are extremely expensive.
APs aren't about "better" WIFI, they are about features. Better WIFI happens when you have multiple WIFI sources.
Okay, but aside from ubiquiti and more enterprise solutions, You can't roam with your phone.
Meaning, i have a galaxy s9, and i walk from my living room to the bedroom, it won't automatically connect to the ap in the bedroom, but stick to the living room ap.
I found a few apps that fix that, but there has to be a better way, that i just can't find online.

I've read that 802.11r is the solution, but i can't figure out how you enable it on phones.
That is mostly a protocol to renegotiate the keys when enterprise encryption is used where there is radius server involved. It makes it faster to get the keys correct. it does not actually cause the device to roam. All it does is reduce the amount of interruption time while it switches.

I do not think the chipsets actually support it, It is not some software you run this is actually done by the radio chipset itself. It would have to be a special driver and I doubt you can even consider doing something like that on a phone where you can't change the OS itself.

This was done years ago by cisco and it only worked on certain brands of phones not sure the company I was with only used it for VoIP because they used to change for all cell minutes. There is almost no need for so called seamless roaming any more.

What most systems do like the mesh things or even ubiquiti is they just force a disconnect from the network side and hope the end device will reconnect to a better source, It doesn't work that well really because the network only knows the signal levels it sees it can not tell what the end device see.

In a home situation all you need to do is stop and start the wifi client and it will generally connect to the best source.

Wifi was never designed for roaming unlike cell networks where the network is in full control of the clients.