There is currently zero traffic over the Kerch strait bridge.

any realistic estimate of how this will effect the Russian supplies and for how long

My understanding is that the rail bridge is presently still in operation, though as things stand, my guess is that they can still use freight rail to get military supplies across the bridge, and then transfer cargo that requires truck traffic in Crimea. I dunno what kind of facilities exist in Crimea for transloading cargo, but I assume that there must be some -- if for no other reason, for last-mile traffic within Crimea.

It'll maybe increase latency or costs, but I assume that they can, if necessary, bump civilian traffic off the line, so they can have a full rail line of throughput.

https://www.theguardian.com/world/live/2023/jul/17/russia-ukraine-war-live-crimean-bridge-emergency-traffic-stops-explosion

He said road traffic would resume in one direction by 15 September, and in both by 1 November.

From the images I saw, it looked to me like the bridge under the northern two two road lanes was cut, but that the southern two at least hadn't fallen, though I don't know what kind of structural impact there was. I'm assuming that what Russia is talking about doing is first just reopening traffic on the southern two lanes, and then transitioning that pair of lanes to an undivided road, one lane into Crimea and one lane out, while repairs happen.

That being said, Ukraine has now hit the bridge and taken down spans twice, and I suspect that it wouldn't be too much of a stretch to assume that they have something else cooking and that this won't be the last time that it gets hit.

Whatever they hit the bridge with, they can almost certainly do it again, so I'd say the bridge is goneburgers.

The Ukrainians can certainly hit most of the territory between them and the Azov sea with HIMARS, and most of it with barrel artillery, so getting supplies into Crimea is about to become very difficult.