I think healing or dealing with personal issues is one of the things you'll most likely find on every japanese drama, so here are some that I would recommend:
Dramas about healing, with a little of romance and focus more on other issues than romance itself. Although they are also kind of gloomy but they're good nonetheless.
https://mydramalist.com/5465-itsuka-hi-no-ataru-basho-de (slow paced but highly recommended)
https://mydramalist.com/1295-last-friends (sick romance but tooons of healing)
https://mydramalist.com/65-sunao-ni-narenakute
https://mydramalist.com/2315-deep-love
Dramas that center on healing or overcoming personal issues, but romance plays a bigger role.
https://mydramalist.com/6425-the-liar-and-his-lover (Movie. Highly recommended)
https://mydramalist.com/31556-hajimete-koi-o-shita-hi-ni-yomu-hanashi
https://mydramalist.com/160-innocent-love
https://mydramalist.com/18788-seisei-suruhodo-aishiteru
https://mydramalist.com/29285-takane-no-hana
https://mydramalist.com/568-summer-snow
https://mydramalist.com/52565-yameru-toki-mo-sukoyaka-naru-toki-mo
https://mydramalist.com/7216-manatsu-no-merry-christmas
https://mydramalist.com/782-beautiful-life
Dramas that have a lot of healing but definitely no romance. Although it is not needed as they are much more about family, mistery and drama. Actually if you don't mind not having romance at all, I would say these are the most recommended.
https://mydramalist.com/102-ryusei-no-kizuna
https://mydramalist.com/3938-w-no-higeki-2012
https://mydramalist.com/646-aishiteru
And not japanese but I think it also has the things you mention xD
https://mydramalist.com/27651-barcelona-a-love-untold
And those are the ones that come to my mind now. Hope it helps!