Both PPTP and L2TP are enabled in the router
Please make sure that you enabled L2TP passthrough, helper or ALG.
The TP-Link Archer AX50 has a built in VPN server, too, which you could use for example for connecting your cottage’s surveillance cameras to your home network.
In other words, make sure Advanced → VPN Server → PPTP VPN is disabled. That will just hog even more resources away from your laptops.
Lets say, if VPN provider supports both the VPN types, does it work switching one laptop to use PPTP VPN type while the other to L2TP?
Yes, this would work. However, most businesses do not allow using PPTP, because it is no longer considered secure.
You should disable VPN in router
PPTP, L2TP and IPsec VPN clients and servers, yes, they should be disabled.
But PPTP, L2TP and IPsec ALG should be enabled.
and install some VPN client in both computers.
I think this is exactly what @mohan is doing.
If he would have a physical IPsec router provided by his company, there would be only a single VPN connection for all work related devices. Thus he would not have a problem of multiple simultaneous VPN instances in the first place.