SIgh.. so many expensive solutions listed here. 8 speed Claris should produce reliable accurate smooth shifting for many years. It is heavier and won't last as long as the top-end gear, but it is a great bargain, and works fine.

First, check for pilot error. For both front and rear shifting, there should be little to no tension on the chain at the moment of shifting. That is, you are pedaling along applying torque to the crankset and tension on the chain, and at the moment of shifting, you ease up on the torque. You don't stop pedaling, but you reduce the RPM slightly at the instant the shift occurs. If you apply full torque during the shift transition, the shift action is slow, noisy, and chews up the drivetrain.

On the front derailleur you cannot just tap it (well, except for electronic), you need to hold the shifter lever or blade down until the chain is lifted up to the big ring. This transition takes less than a second. We've had clients come into the shop repeatedly with undiagnosable front shifting problems and it turns out they expect the shift to the big ring occurs by just lightly tapping the shifter blade.

Mechanical stuff: get a pro mechanic to run through the gears from scratch. Check the chain and the rest of the drivetrain. Change out all of the housings and cables if necessary; this is inexpensive stuff - a lot cheaper than a drivetrain swap or a new bike! All of Shimano's road stuff is good, and should shift like butter.