Here's some steps to follow when you can’t find a part in Studio.
First, know that there’s different numbers that identify a part.
LEGO uses two numbers: a Design ID (4 or 5 digits) that codes for the shape of the part and an Element ID (7 digits) that codes for a combination of shape and color. The Element ID is the number printed in the list of parts at the end of official instructions.
BrickLink and Studio use an Item Number: it’s generally based on LEGO’s Desgin ID but as LEGO may use different numbers for the same part or the same number for different variants and as BrickLink prefers to keep the same base number for plain and decorated parts, they are often different.
For now, Studio only uses the BrickLink Item Number. So search the part on BrickLink to be sure of its ID, or try searching it by its BrickLink name:
If you can’t find a part, check that you are looking in the Main palette, that you aren’t filtering the parts in the palette by color or by decoration.
Then, it means Studio doesn’t officialy have this part yet :( You can check in the community’s part repository if the part is in preparation. You may also check on LDraw’s part tracker if a 3D model is availailble, so you can import it with PartDesigner. Finally, you can ask on the forum for the part to be added.
A more complete and more technical explanation is available on the forum’s Parts FAQ.