As a longtime Shen main I too miss old Shen, but I have gotten used to new Shen's kit. With old Shen I would regularly have highest damage dealt, with new Shen I almost always have highest damage mitigated (in lengthy games it can go up to 100k). New Shen definetly can still beat adc's caught out alone, but you gotta land that taunt. Old Shen braught good HP regen in his Q which I liked, his old passive was also extremely good and made him more bursty. New Shen is more DPS and skillful since you need to proc that Q, his passive is clunky af and it took me ages to be able to comfortably use it (still hate that it isnt instant).
Something cool you can do on Shen if you are vs a extremely hard counter (you cant hope to win lane), run Guardian and revitalise, ultimate hat with transcendence. You will have a extremely powerful ult, getting + 100/200 shield and ms boost on your ult, increasing shield strength by 15% if they are lower than 40%. Thats about a 437 shield if they are below 40% on level 1 (280 if max health), both of those value's are higher than what they ever been.
Say you have +2000 bonus health at level 3 ult, you hit almost 1300 shield on 40% allies (866 on full health). These are extremely good values, and are higher than prenerf ult stats. With 25% cdr at level 2 ult, you can ult every 135 seconds and once every 120 seconds on level 3. Respectively bringing his level 2 ult to a lower CD than prenerf, and his level 3 to pre-nerf levels.