Are you asking about roads within Yellowstone, or state roads going around it. The big flooding news last year was on the north side of the park, the north entrance through Gardinier, US89. That was washed out in many places. I haven't kept up with repair or reroutes. Maintaining access to Gardinier and Cooke City is a winter priority.
I also recall flooding images around Red Lodge on US212, but I don't think that was severely damaged. US212 is closed for the winter, with a late opening.
The Google Maps closures in the park mention either April 5 or May 26 for opening. Other than 212, I don't see any closures outside the park.
ON the park's road conditions page the only mention I find about flood damage is
Northeast Entrance Road (Flood Recovery)
Location: East of Tower Junction between Lamar Canyon and the Northeast Entrance
Access: Expect up to 30-minute delays beginning early summer 2023 through fall 2023.
Improvements: This project includes the completion of work to address flood-damaged areas of the Northeast Entrance Road. Construction will include completion of a two-lane realignment in Lamar Canyon, paving a second lift north of the Trout Lake Trailhead, stabilization of streambanks adjacent to the road, and work in the Pebble Creek Campground and Warm Creek Picnic Area. Additionally, some guardrails, culverts, and other drainage structures will be replaced.
The rest looks like the usual winter reopening details.