I've only tested this skript in 1.8.x, but it should work in 1.16. Enjoy.

Code (Text):

1. on damage of player:
2.   if attacker is a player:
3.     if {combat.%attacker%} is not set:
4.       send "&c&lPVP &7» You are now in &cCOMBAT&7, don't log out!" to attacker and victim
5.     set {combat.%attacker%} to true
6.     set {combat.%victim%} to true
7.     set {combat.%attacker%.lastHit} to now
8.     wait 30 seconds
9.     if {pvplog.%attacker%.lastHit} was more than 29.9 seconds ago:
10.       send "&c&lPVP &7» &7You are no longer in &cCOMBAT&7." to attacker and victim
11.       delete {combat.%attacker%}
12.       delete {combat.%victim%}
13.       delete {combat.%attacker%.lastHit}
14.  
15. on quit:
16.   if {combat.%player%} is true:
17.     broadcast "&c&lPVP &7» &c%player% &7Combat Logged, and got killed!"
18.     Kill player
19.     set {pvp.logger.%player%} to true
20.  
21.  
22. on join:
23.   if {pvp.logger.%player%} is true:
24.     delete {pvp.logger.%player%}