While the connections are "guaranteed" the way they are protected varies based on how late the incoming train is, how many people are making a given connection, and alternative transport availablity.
Best: train makes it and Amtrak personnel hustle you from one platform to the other.
Better: incoming train is only about 30 minutes or less late, and a lot of people are making the connection. They hold the outbound train for connecting passengers.
Okay: bus bridge to catch up with outbound train. Example, busing Starlight to Sunset connecting passengers from Oxnard to Palm Springs. Note depends on ability to charter a bus at relatively the last minute.
Okay: Alternative Amtrak service. Example, Late SW Chief or Sunset passengers to NorCal and points north missing the Starlight are put on the San Joaquin/Bakersfield Thruway bus connection to their destinations or to catch up with the Starlight at Sacramento, Martinez or Emeryville. Passengers to points further south are put on Surfliners and its bus connections.
Not so great. They put you up in a hotel and modify your reservation to the next day's train. Note if you have sleeper reservations and sleepers are sold out on the next day's train, you will be put in coach and your sleeper accommodation charge refunded. Note this is an special danger for you because if the Washington, DC connection is missed, they will rebook everything, Capitol, Zephyr and Starlight (assuming you built in no layovers). This time of year if you had sleepers, your chance of losing them on at least some if not all segments is quite high.
Worst: they can't accommodate you, refund your fare and you are on your own. This does happen, but not often. It happened to me back in 90s when the Builder missed a three day a week connection to Indianapolis. They gave me money in Chicago and sent me on my way. That is unlikely in your case.
I have been laid over overnight several times.
Finally, note that Amtrak has been having much more difficulty than it used to arranging last minute bus charters, probably due to the "great resignation" and capacity in bus companies having been reduced during COVID. Also, in comparing the north and southbound schedule there appears to be only about 10 minutes of pad between Richmond and Washington.
If I were you, I would be concerned about that DC connection. My own semi-educated guess is if that connection is missed by more than they'll hold the Capitol for, they'll lay you over, they won't bus you. You should probably look up the connection history on ASMAD.
The good news is I wouldn't worry too much about the Chicago and Sacramento connections. The danger point is DC.
