Just a little survey. What's your WAN interface MTU and maximum ping size? I'm more interrested in IPv6 just to make sure that I'm interpreting PMTUD and hidden costs right. Try increasing or decreasing (-s parameter) it until you get maximum working size.
MTU: 1492
IPv6 caps at 1436:
ping 2001:4860:4860::8888 -M do -s 1436
PING 2001:4860:4860::8888(2001:4860:4860::8888) 1436 data bytes
1444 bytes from 2001:4860:4860::8888: icmp_seq=1 ttl=111 time=27.3 ms
1444 bytes from 2001:4860:4860::8888: icmp_seq=2 ttl=111 time=30.4 ms
1444 bytes from 2001:4860:4860::8888: icmp_seq=3 ttl=111 time=35.8 ms
1444 bytes from 2001:4860:4860::8888: icmp_seq=4 ttl=111 time=27.7 ms
1444 bytes from 2001:4860:4860::8888: icmp_seq=5 ttl=111 time=32.2 ms
^C
--- 2001:4860:4860::8888 ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4006ms
rtt min/avg/max/mdev = 27.290/30.674/35.809/3.129 ms
IPv4 caps at 1464:
ping 8.8.8.8 -M do -s 1464
PING 8.8.8.8 (8.8.8.8) 1464(1492) bytes of data.
1472 bytes from 8.8.8.8: icmp_seq=1 ttl=107 time=36.5 ms
1472 bytes from 8.8.8.8: icmp_seq=2 ttl=107 time=36.0 ms
1472 bytes from 8.8.8.8: icmp_seq=3 ttl=107 time=34.3 ms
1472 bytes from 8.8.8.8: icmp_seq=4 ttl=107 time=30.9 ms
1472 bytes from 8.8.8.8: icmp_seq=5 ttl=107 time=33.3 ms
^C
--- 8.8.8.8 ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4006ms
rtt min/avg/max/mdev = 30.898/34.189/36.490/2.002 ms
The optionally installable tracepath serves you the path MTU on a platter, without requiring to play ping games:
root@ router:~# tracepath -4 -b 8.8.8.8
1?: [LOCALHOST] pmtu 1492
1: loopback1.0001.acln.01.ahr.de.net.telefonica.de (62.52.192.240) 28.011ms
1: loopback1.0001.acln.01.ahr.de.net.telefonica.de (62.52.192.240) 94.011ms
2: bundle-ether4.0002.cord.01.ahr.de.net.telefonica.de (62.53.11.234) 500.010ms
3: bundle-ether20.0003.corx.01.ham.de.net.telefonica.de (62.53.5.76) 878.011ms asymm 7
4: bundle-ether3.0002.cord.01.ham.de.net.telefonica.de (62.53.6.183) 592.011ms asymm 6
5: ae1-0.0001.corp.01.ham.de.net.telefonica.de (62.53.12.35) 525.010ms
6: 74.125.48.102 (74.125.48.102) 115.010ms
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Too many hops: pmtu 1492
Resume: pmtu 1492
root@router:~# ping -M do -s 1464 -c 1 -4 8.8.8.8
PING 8.8.8.8 (8.8.8.8) 1464(1492) bytes of data.
1472 bytes from 8.8.8.8: icmp_seq=1 ttl=117 time=11.5 ms
--- 8.8.8.8 ping statistics ---
1 packets transmitted, 1 received, 0% packet loss, time 0ms
rtt min/avg/max/mdev = 11.542/11.542/11.542/0.000 ms
root@router:~# ping -M do -s 1465 -c 1 -4 8.8.8.8
PING 8.8.8.8 (8.8.8.8) 1465(1493) bytes of data.
ping: local error: message too long, mtu=1492
--- 8.8.8.8 ping statistics ---
1 packets transmitted, 0 received, +1 errors, 100% packet loss, time 0ms
root@router:~# tracepath -6 -b 2001:4860:4860::8888
1?: [LOCALHOST] 46.000ms pmtu 1492
1: 2a02:3001::20a (2a02:3001::20a) 995.009ms
1: 2a02:3001::20a (2a02:3001::20a) 253.010ms
2: 2001:4860:1:1::ff1 (2001:4860:1:1::ff1) 766.011ms
3: 2001:4860:1:1::ff0 (2001:4860:1:1::ff0) 151.010ms !A
Resume: pmtu 1492
root@router:~# ping -M do -s 1444 -c 1 -6 2001:4860:4860::8888
PING 2001:4860:4860::8888(2001:4860:4860::8888) 1444 data bytes
1452 bytes from 2001:4860:4860::8888: icmp_seq=1 ttl=120 time=11.1 ms
--- 2001:4860:4860::8888 ping statistics ---
1 packets transmitted, 1 received, 0% packet loss, time 0ms
rtt min/avg/max/mdev = 11.127/11.127/11.127/0.000 ms
root@ router:~# ping -M do -s 1445 -c 1 -6 2001:4860:4860::8888
PING 2001:4860:4860::8888(2001:4860:4860::8888) 1445 data bytes
ping: local error: message too long, mtu: 1492
--- 2001:4860:4860::8888 ping statistics ---
1 packets transmitted, 0 received, +1 errors, 100% packet loss, time 0ms
There seems to be an additional tunnel header in-band for IPv6, around 8 bytes on your link...
This is what I was trying to figure out. Thank you for the reply!
I guess you should (if possible) talk to your ISP.
Actually I shouldn't. Their official MTU is limited to 1480.
When running a torrent, the VLESS connection to the server via Podkop is disconnected - thanks to this topic I found out my ISP doesn't wipe DSCP marks (at least bulk). It was not the case before. Also I found that not only they support 1492 (at least for IPv4) but mini-jumbo as well. PPPoE debugging shows that they still advertise 1480. Now I'm in the mood of poking them even more 
Well, your know your ISP better. That likely means we will never learn what the root cause is.
Probably I should just wait when their box will get fried by another lightning strike. Last time it happened they upgraded me to IPv6