Why do we supplicate to Allah as long as He does what He wills and gives to whomever He wills? Is there any harm in suffice oneself with worship without supplication, if everything is predetermined?

We supplicate to Allah despite our knowledge that everything is predestined for three reasons:

Firstly: Because Allah loves to see us humble and supplicating. This is an manifestation of our utter dependence on Him, and it is one of the acts of worship He has commanded us to perform.

Secondly: Because Allah has predestined things with their causes. Supplication is one of the means He has commanded us to employ to achieve what is desired, just like striving to seek sustenance. For Allah does not predestine the outcome alone, but rather He predestines it along with its cause.

Thirdly: Because supplication grants us more of Allah's bounty. Either Allah answers the prayer in this world, or He stores it for us in the Hereafter, or He diverts from us an equivalent amount of evil. Supplication never fails; it either achieves the desired outcome for which it was made, or it becomes a cause for reward, or Allah substitutes for the supplicant something better than what he prayed for.