Welcome! Sorry no one saw or responded to your post earlier. New posters often are held up in moderation for a few days, and can get lost in the shuffle.
I'm sure others will chime in with their experiences, but I'll just start off with my high-level criteria for these kind of questions: is your daughter healthy, happy, and growing? Does she feel loved and secure? Are you following her lead with her intellectual and other interests, or are all these enrichment activities adult-motivated?
At her age, learning should feel like play. At the same time, "failure" should be a common and unremarkable opportunity to develop and problem-solve, much like falling is typically a common and unremarkable part of learning to walk. Pressing her to attempt things that distress her is certainly not required (possibly with rare exceptions related to safety), but it can help to model, verbally and visually, the process of failing and trying again as a normal and healthy part of life at every stage of life.
