Apparantly TxDOT does want to turn 290 into a Freeway out to Dripping Springs
No, they don't. Rather TX DOT wants to extend the US-290 freeway to Hays County Acres Road. From that point going West they would intend to build a bypass around Dripping Springs. The diagram list of over-passed intersections in the PDF mention a "northern bypass" West of Hays County Acres Road. But it's anyone's guess what kind of alignment a US-290 freeway around Dripping Springs would take. One thing is certain: there is too much development within Dripping Springs to upgrade the existing US-290 alignment into a freeway flanked by frontage roads.
Additional freeway upgrades of US-290 out West of the Oak Hill Y Project (which will end just West of Circle Drive) are necessary. Traffic gets pretty heavy on US-290 thru Dripping Springs.
On top of US-290 issues TX DOT or whatever toll road authority that oversees TX-45 needs to work on building out that corridor to connect to the TX-45 segment on the East side of I-35 and extend it West to US-290. That way TX-45 can act as a proper relief route move a good amount of thru traffic around the South side of Austin.
San Antonio and Austin are slowly but surely (in case they aren't already) becoming a Megapolis with San Marcos and New Braunfels in between, meaning more traffic in the future
San Marcos and New Braunfels are among the fastest growing regions in the US. Few places can match that growth. Maybe Northwest Arkansas and the "triangle" area in North Carolina might be in contention. Around 5 million people now live in the combined Austin and San Antonio region. By 2030 it could be over 6 million.
Make US-290 a freeway could possibly reduce (and possibly divide) the traffic on I-10 and I-35 north of San Antonio
Austin is a big enough city that it needs its own East-West Interstate (nearly 1 million city limits population and 2 million metro). IMHO, the US-290 corridor should be upgraded West from Austin to I-10 out West of Fredericksburg. East of Austin multiple corridors will eventually need upgrades between I-35 and I-10 if rapid growth continues over the next 10, 20 or more years. US-290, TX-71, TX-80 & TX-46 will all needs lots of upgrade work.