How can i perform deep filtering from the components value?

Get in mind that you can use filters while populating the repeatable components.

Your solution will like this after adding the filters while populating your repeatable components.

// your existing code

populate: {
                planBlock: {
                  filters: {                        // add filters for repeateable component here while populating
                    date: date,  
                  },
                  populate: {
                    plans: {
                      populate: {
                        train_pages: {
                          populate: {
                            image: true,
                            equipment: true,
                            author: true,
                          },

// Your remaining code

For more reference on advanced populating: https://docs.strapi.io/dev-docs/api/entity-service/populate#advanced-populating

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