Is there any Sharia impediment to the company reimbursing medical expenses and requiring registration in its private health insurance system—given that insurance subscriptions have ceased—and to the reimbursement of invoice values in Euros when treatment is received outside Libya, for collection from a bank in Tunisia?

No শরعي (Shar'i) prohibition is apparent in the questioner's utilization of health insurance, and the responsibility for renewing subscriptions lies with the employer. There is no harm in transferring money abroad in a currency different from that due in the invoices. If there remains any surplus after settling the dues, its return or retention by the employee is subject to the company's management.