Your area gateway has a very much optimized routing. Correct MTU set also. Nice.

Nope, they didn't do any of that. They just read the packet TTL and derive it from the OS because different OS has different default TTL.
If TM want to game the website they can just MPLS from the BNG.
But wait for it, I can do it myself and the internet is so much smoother after that!

Take a chill pill man. Be calm mate. I thought it was plusminus 8 bytes. Now 12 bytes meh? Maybe I need to refresh my networking knowledge. I think I didn't mention about routing problem for me. I just shared the browserleaks.com/ip stat for fun. Maybe you wrongly tag me mate.

Now hop count  is not accurate in MPLS network. I already written it few days back to Ashren but he didn't rebuke any of my technical explanation. I will repeat the gist here.
In MPLS network, a single tunnel will reduce TTL by 1 hop, regardless of if it pass through 1 router or 100 routers. Compare to path that didn't enter MPLS tunnel, each router is considered 1 hop. This is also the reason why I have written in the past about local telco should provide BGP Looking Glass which at least shows the MPLS Label routing.

What do you mean? TTL is a required headers for all packets, regardless of it's TCP, UDP or ICMP.
There's no such thing as main gateway as every router along the path is technically a gateway. But not all of them will reduce the TTL by 1, in the case of MPLS.
Now there's no way for the web site to know how the packet route at all, including if it went through a tunnel.

Is there a gateway that don't run IP? I am not sure what do you mean.

Is that a question or a statement? Every gateway process TTL. Every gateway runs IP.

Sorry man, I think my brain is having some problem. I still don't quite get your question.

If your question is "Is the hop count accurate if your telco don't use MPLS?"
The answer is most probably not. When your packet crosses to another AS, that AS might very well use MPLS / SRv6 in their network. This is a common deployment pattern used by a lot of service provider called "BGP-Free Core".
The implementation can be straight MPLS, Control-plane using MPLS with data-plane using SRv6, or straight SRv6, but the concept is still the same, with the same implication.

If your question is "Telco use MPLS routing, but you do not know if you are crossing a MPLS segment, which TTL is used?"
MPLS header has a TTL field. If it crosses the MPLS segment, the TTL field in the MPLS packet will be reduced. But your packet is never processed because it is the payload inside the MPLS packet.
Once the packet exit the MPLS tunnel, then processing of your packet from subsequent routing decision will reduce the TTL from your packet. Of course this also applies when the packet leave your device because MPLS tunnel don't exist in your home network.

Let's say none of all the above is true, we still might have a situation where MPLS tunnel is encapsulated inside another MPLS tunnel. This is a common scenario called "carrier of carrier".

MPLS will encapsulate anything, it just treat the payload as data stream. So for TTL Propagation to work, it will specifically recognize IP packet only.
In the first encapsulation, you have the following:
MPLS(IP)

In second encapsulation, it becomes:
MPLS(MPLS(IP))

You can keep on encapsulating as long as your network has a big enough frame size. So as you can see if you only go through one MPLS tunnel, your IP packet TTL will reduce just fine (assume the router is configured for it). However when it hits another tunnel, the data type of the payload is MPLS, not IP, so TTL propagation stops.