What is the ruling on settling the expenses for fitting out a commercial shop after the closure of a project that was a partnership with a relative, knowing that the fittings are still present in the shop?

The transaction mentioned contains an element of ignorance (jahalah) and gharar (uncertainty), because the wage is an undivided share of the profit, which makes it unknown, and this is impermissible. Therefore, this unlawful transaction must be dissolved. You are entitled to what you contributed in terms of equipment, and you are entitled to the customary wage (ujrat al-mithl) for the period you occupied the premises, because a فاسد (invalid/corrupt) contract warrants the customary wage, as mentioned by Zakariya al-Ansari and Ibn Taymiyyah.