Remote work from an EU country for a company based in Malta

I cannot comment on the Maltese legal viewpoint of the matter, but here is the German one:

1. Residence: You are EU national due to your profile, so there are no visa and permit issues. But you need to properly register the German address you live at - and become member of a German health insurance.
2. Work: Since you have no German employer, you will be classified as self-employed, have to register a business and do all accountancy, licensing (if applicable) and taxation tasks on your own - or, if you aren't fluent in legalese German, engage professionals for this (at a fee). You also must pay all dues to health insurance and potentially other social security schemes from your own pocket (usually, the employer pays half).
3. Taxes: Residents of Germany are by default tax-liable here with their entire world income. Bilateral tax-treaties (which might exist with Malta, so check!) reduce the incidence of double-taxation by typically giving the right to tax salary to the country where the work is performed (Germany, in your case) and passive income (e.g. property rents) to where it accrues. But you have to declare your entire world income in Germany in any case, because it is used to calculate the tax rate applied to the German-taxable portion (this is called "Progressionsvorbehalt") - and because it's the tax authority, not you, who decoides what is taxable here and what not.

Altogether, as we have written many times on this forum (the topic pops up often!), these costs and complications make working remotely in Germany unattractive in most cases.