Option 3-1: single TP-Link Archer AX72
A simple upgrade below S$100 -- you can get TP-Link Archer AX72 (AX5400 rated), BNIB from Carousell at around S$80 to S$90 (dumped by M1 users).
Then replace your Singtel Mesh Extender 1 with the TP-Link Archer AX72. It should be able to sort out wireless access issue for your Laptop 1 and 2.
I will still recommend to add a switch in Bedroom 3 for your PC and Laptop 1. Wired connection is always better when it is possible. TP-Link TL-SG105 is below S$30.
You can then put the Singtel Mesh Extender 1 in Bedroom 2 if needed.
You can try to set up TP-Link Archer AX72 in AP mode and then using the same SSID and password as your Singtel Mesh Extender. Then you check whether if your mobile device is having issues in BR3/BR2/MBR or not. If not then that is good. If there is an issue then you have to use a different SSID.
Option 3-2: 2 units of Asus RT-AX55
For mesh solution, based on your lower budget of around S$200, you can get two units of RT-AX55 from Carousell (around S$70 to S$80, dumped by M1 users). That should give you better roaming performance. You can start from two units, replacing the two Singtel Mesh Extenders. Single unit of RT-AX55 is not as powerful as TP-Link Archer AX72 but two units will give you the benefits of forming a mesh (AImesh) for better roaming performance.
Option 3-3: 2 units of TP-Link Archer AX73
Edit to add: now TP-Link Archer AX72 is able to support EasyMesh (mesh with itself), so you can get another Archer AX72 and put it inside either BR2 or BR3. In this case you can get rid of two Singtel Mesh Extenders.
Reference:
https://www.tp-link.com/sg/support/faq/3529/