The nice thing about a Tioga Pass choice is you don't need to make it until late in the trip since it wouldn't be much of detour from the Western Express route.
I love Yosemite - and have biked / hiked it many times.
One trip, the concession services took my bike & gear up to Tuolumne and I hiked up the John Muir Trail.
But this year is different - record snowpack. Likely to be significant damage after snowmelt.
Double-edged sword:
a) A slower snowmelt will easily go into July.
b) A fast snowmelt will result in flooding with even more damage.
Historic opening/closing dates of Tioga Pass -
https://www.nps.gov/yose/planyourvisit/seasonal.htm
Note that in 2017 & 2019 with 176%-177% of average snowpack
Tioga Pass opened on June 29 & July 1.
This year snowpack is 237% of normal.
Not to mention that people go out onto fragile, waterlogged meadows despite signs saying "No Entry" -
Or camp illegally when bears are struggling to gain weight after a prolonged winter.
So, park officials usually err on the side of caution.
I don't think Tioga will open before July 14.
And, if there is considerable damage, the road may open,
but facilities will remain closed for the entire season.
Which makes it extra challenging for cyclists.