Looking for a Time Travel novel I read some 20 years ago

I’m trying to find a book I read around 20 years ago with a unique time travel plot. Here are the main points:

The protagonist works in an agency during the third age of time travel. This agency’s primary mission is to clean up the messes made by time travelers from the earlier ages.

As the story unfolds, it’s revealed there are multiple ages of time travel, more than initially believed.

At one point, the protagonist gets trapped in a time loop and discovers a room filled with the dead bodies of his past selves.

In the climax, we find out that the protagonist originates from the very last age of time travel and was created by an AI.

Does anyone recognize this plot? I’d love to find this book again.

I do remember that the book included even more hilarious novel, where protagonist influences the probability of events, like finding a vending machine in the middle of the desert. But due some scientifically explained magic, this power only worked when he was touching salami socage. In the and he was falling from the tower bagging for any miracle with some salami in his hand and a gust of wind dropped him right through a window on the main villain’s head.

I need to re-read this awesome stories and recommend them to everyone.

by TeachingSenior9312