To be honest, Seattle taxes for Metro Transit aren't part of the gasoline tax. They put that on the sales tax percentage and maybe as an add-on to vehicle taxes and maybe even an addition to property taxes. Since we don't live there, I can't be sure.
I think the gas tax increase is to pay for road and other infrastructure improvements. Goodness knows, the Seattle metropolitan area needs megabucks to solve its traffic woes. For those of us out in the dingle-weeds, their problems are none of ours, except the gas tax increase will affect us all. It may run us off the RV life-style - it's marginal already with the price of gas.
When I worked for Skagit Transit (75 miles north of metropolitan Seattle) we got the county taxpayers to approve a small increase in the sales tax to keep the system running. It's a very conservatively managed agency that provides useful service to the county, and works within its budget. The residents are favorably inclined.