they may be the same sensor, but they have different wiring and different part numbers. look them up at rock auto parts. IF you replaced one sensor last year, replace the other now.
the shaking up front concerned me, and bad shocks can ruin a set of good tires. if the shocks are bad, get them fixed first before sinking money into the tires. I know because ruined new tires when the shocks were bad on my ES330 at 90K.
my son, an attorney, was over the other day. Out of the blue he said to me, why don't you buy a new car and give me the Lexus. Well, I still love the car even it is an 05. It is great on the road and gets 28 or so MPG. I didn't reply to him.
bearing noise in the motor at 137K , and figured it was alternator, as the charging voltage was 12.1. got one at local parts store, and took it to mechanic today. 33 minutes later he was done! you don't have to take off the larger bracket held in with the 2 14mm bolts to remove the alt. There is youtube video showing this removal, so it easier than this video shows
you might try deleting all the codes to see if taking it out of "safe" mode will help. i'd change the 02 sensor also. can't see how changing thermo. would affect the coil or other electrical things as long as you plugged everything back in correctly.
I own the same car, and avoid pushing hard on the pedal, do most accel. in 3rd. gear. this is a known problem and cleaning the fuel system is not needed. I accelerate using the cruise lever often, and know there is lots of power at 3200rpm.!
ATF fluid levels are checked after going through all the gears. I have lexus ES330, and have done 5 drain and fills in 135K miles on this car. Just did it on our Rav4 with the WS fluid and I drove some on a 90 degree day, and the fluid was above the upper limit, perfect. 3.5-3.6 qts. is what came out. good job on your flush!
rockauto parts has good cheep relays
https://www.rockauto.com/en/catalog/lexus,1998,es300,3.0l+v6,1316093,electrical-switch+&+relay,a/c+system+relay,13364