Which languages should a Turkish manufacturer publish in?

The default answer is Turkish and English, and it is usually wrong — not because those are the wrong languages, but because the decision was never made. It was inherited.

Start from the export ledger, not the map

The languages worth publishing in are the ones your existing buyers already purchase in. That information is in your own invoices. A manufacturer whose shipments go to Russia, Central Asia and Germany has a different answer from one shipping to the Gulf, and neither answer is discoverable from a list of the world’s most-spoken languages.

Then look at what your competitors have not done

The second criterion is neglect. English is table stakes and every competitor has it, so it wins nothing. A language your competitors have skipped is a market where a buyer searching in their own language finds you and not them. In practice this is frequently Russian or German for Turkish industrial exporters, and the reason is simply that both take real effort to do properly.

A language is not a translation

A language edition means the technical terminology is correct in that language, the URL structure is separate, hreflang is annotated so search engines serve the right version, and the enquiry form routes to someone who can answer in it. A machine-translated menu over Turkish product pages is worse than not offering the language, because it advertises a capability the company does not have.

The maintenance question

Every language multiplies the cost of every future content change. Four languages means a new product is four pieces of work. This is the real constraint, and it is the reason to choose two languages you will maintain over five you will not. A stale edition is a liability.