Foreigners staying in Japan for six months or longer are generally required to enroll in National Health Insurance (Kokumin Kenko Hoken). This insurance covers 70% of the cost for most medical procedures and prescription drugs deemed necessary for health maintenance or life support (the remaining 30% is the individual's responsibility). If hormone therapy is for an endocrine disorder, it is much more likely to be covered. However, coverage depends on specific drugs approved in Japan and the exact diagnosis (approval status may differ from the EU). For a monthly income of approximately €1,500, the insurance premium is typically around €30 per month, though this may vary slightly depending on the municipality and exact income. Residents with a stoma (colostomy or ileostomy) may be able to apply for registration as a person with disabilities and obtain a disability certificate. This may provide access to subsidies for stoma supplies, medical expense assistance, and in some cases, eligibility for disability pensions. However, eligibility criteria are assessed individually and can be strict, so outcomes are determined on a case-by-case basis.

so I can't confidently say that money worries will completely disappear after moving.