With the current schedule, unfortunately, Train 529 would be the latest option available to get you to the airport in a reasonable amount of time. This train currently averages about 12% occupancy. Schedule out of SAC at 7:33am, arriving to RIC at 8:59am. From there you can walk down from the Amtrak station into the BART Station and go through the BART faregates and up to the BART platform. There are two BART route options that would both require transfers.
The option BART will tell you to do is a Orange (Berryessa) Line train to MacArthur and then make a cross platform transfer to the Yellow (SFO) Line train. Another option if you'd like to have more of a chance of spacing would be the Red (Millbrae) line train to San Bruno and then a same platform transfer to a Yellow (SFO) Line train one stop to SFO. Berryessa trains leave Richmond at :03 and :33 after and Millbrae trains leave at :11 and :41 after. Depending on your transfer the ride takes just over an hour from Richmond to SFO with the transfer. The average ridership at the time you are riding is approximately 13 passengers peak per car on the Yellow Line and 9 passengers peak per car on the red line.
BART no longer sells paper tickets from their vending machines so the machine will only sell you a Clipper Card now. The Clipper Card is $3 in addition to the BART fare. The machine will give you the total amount. Not all Machines take cash so if you are using cash be sure to look for one that does. The Station Agent should be able to assist you if you have any questions.
The Capitol Corridor allows two pieces of carry on luggage plus two personal items such as a backpack or small bag. Carry-ons should not exceed 28 x 22 x 14 inches or 50 lbs. Personal items should not exceed 14 x 11 x 7 inches and 25 lbs. Luggage racks on most of the cars will be upstairs near the stair case. There are small overhead bins above the seats but on most cars (8000-series) they are very small so they don't fit much. There is space behind some seats or on the lower level as well if seated there. The luggage racks by the entry doors are usually folded up for bike rack space though they may sometimes be available. The policy is one ticket, one seat so they request bags not be placed on an adjacent seat. I haven't personally ever had an issue with luggage though and the trains for the most part have been fairly empty with room to spread out a bit.
Face coverings will be required on all the trains and in all the stations you will be traveling to. The only exception is when actively eating or drinking though that isn't allowed on BART. The café cars are closed on the Capitol Corridor, however they usually have a little self-serve snack bag and small bottle of water if needed. Those are complimentary while café car service is suspended and are located on the counter within the café car itself.
I believe that covered most of your questions. Richmond BART is not the greatest, however it is generally fine during the daytime with the brief connection time you have. This is the most direct option. Just know this will most likely put you at the airport between 10am and 10:30am so you will have quite a bit of time before your flight. With the COVID schedule, the next Amtrak train (537) isn't until 12:14pm from SAC, however you wouldn't get to the airport until closer to 3pm assuming all the connections worked. Hope it works out and you enjoy your trip.
Capitol Corridor
BART