I know most of the lore for the game so far, but does any explain why it is reasonable for the characters to fight, if they always just respawn a few seconds later and rejoin the fight?
The confrontations that happen in PVP matches are not canon. They're framed by the lore, but they can include clearly nonsensical things (Like 6 Lucios battling against another 6 Lucios). Certain characters have 0 reason to work together, like Tracer and Widowmaker, yet gladly do so.
Until we see otherwise, there's no reason to assume these PVP games are actually occurring in the Overwatch timeline. Think of it more as providing a backdrop.
Some of the characters, upon respawn, make mention of "the wonders of modern medicine". This is probably the best you will get for an explanation of the respawning in-game.
There is one hero which the lore of OW does sort of support infinitely respawning -- Reaper:
Reyes resurfaced as a volatile mercenary known as "Reaper." His identity and motives remained unknown. Now a ruthless and remorseless killer, he was responsible for terrorist attacks throughout the world. He fought in many armed conflicts over the decades, showing no loyalty to any cause or organization. Survivors described him as a black shadow ghosting unscathed through the most hellish battlefields. The few bodies recovered of his victims were pale, empty husks drained of life, their cells showing signs of intense degradation. It was speculated that Reaper was a byproduct of failed genetic alteration which forced his cells to simultaneously decay and regenerate at a hyper-accelerated rate.
Those attempting to track his movements began to see a pattern in his appearances. They believed that Reaper was hunting former Overwatch agents and systematically eliminating them.
Keywords from the summary:
speculated that Reaper was a byproduct of failed genetic alteration which forced his cells to simultaneously decay and regenerate at a hyper-accelerated rate.
This, in accordance with his interactions with Mercy supports that after the bombing of OW HQ, Reaper can constantly regenerate his cells even after he decays. Some quotes after he respawns are "The grave cannot hold me back" perhaps indicating he's done this before.