Healthcare quality for foreigners tends to follow a pattern: major cities in most middle and high-income countries have excellent private hospitals, often with internationally trained, English-speaking doctors, while quality drops noticeably in rural areas everywhere. Several countries in Asia and elsewhere have built entire medical tourism industries precisely because their private care is both good and affordable by Western standards. Public systems vary from world-class to overstretched depending on the country.
On payment, be prepared for the upfront model. Many hospitals abroad, especially private ones, require a deposit or full payment before treatment and then you claim reimbursement from your insurer afterwards, so keep every receipt and medical report. Direct billing to international insurers does exist, but usually only at larger hospitals that have agreements with major insurance networks; your insurer's hotline can tell you which local facilities offer it, which is worth knowing before an emergency.
Two habits protect you: carry your insurance details and a means of payment at all times, and call the insurer's emergency line early in any serious situation, because they can guarantee payment to the hospital and unlock treatment faster.