Do I have to leave the Schengen area if I have a short term (C) visa that will expire right before my National Visa (D) officially starts?

Unfortunately the answer to this question is not completely clear-cut.

From my reading of the actual Schengen legislation, there is no requirement that you leave the Schengen Area while transitioning from your C-visa to the D-visa.

It is common and well known that one can stay within the Schengen area while transitioning between two back-to-back C visas. This is the standard way for things to be, for example, when someone is planning to be in the Schengen area on the day when an already issued multiple-entry visa expires and he applies for a visa to cover the rest of that visit. There seems to be nothing in the rules that imply that transitioning between back-to-back C and D visas should be handled differently.

The reason why I don't call this completely clear-cut is that we have gotten questions about a similar situation, namely a visa-free national wanting to continue a long stay under a D visa as a visa-free short stay in the same or another Schengen state. In that case the rules also do not appear to require a "visa run", but nevertheless we have anecdotal reports of people getting told in advance by border guards, police and the like that a visa run is needed.

I don't think we have any reports of people actually getting into trouble by not doing a visa run on a D-to-visa-free boundary, though.

We also haven't, as far as I remember, seen anyone try to back the need for a visa run with actual references to the text of the Schengen regulations.

The D-to-visa-free situation differs from yours in that one can argue that the traveler needs an entry stamp to show when the 90/180 day clock that governs his visa-free stay began ticking, and the way to get an entry stamp is to exit and enter the Schengen Area. This does not apply to you because the 90/180 rule does not apply to you while you're in Germany under a D-visa. (It applies if you visit Schengen countries other than Germany during the validity of the D visa). So the argument that you need to do a visa run is weaker.

Make of all that what you will. Personally, in your shoes, I would not bother to do a visa run, but it's really up to how risk-averse you are. After all, if you do get into trouble, "a random person on the internet said it would be okay" is not much help.

From my research, you must exit and enter although you have the opportunity to request a change in status without leaving. You can do that by consciously passing through immigration as you cross from wherever you are in the Schengen area into Germany (do that BEFORE the C visa expires).

Typically immigrant status do not just transition from one to the other without some formal approval from authorities to activate the new status. In your case, see the Federal Office for Migration and Refugees (BAMF) or immigration offices for Schengen in the member country where you are located to confirm if the legal framework exists for you to do so.

See Opportunities to change the residence title and the purpose of stay in Germany Focus-Study by the German National Contact Point for the European Migration Network (EMN)

https://www.bamf.de/SharedDocs/Anlagen/EN/Publikationen/EMN/Studien/wp67-emn-wechsel-aufenthaltstiteln-aufenthaltszwecken.pdf?__blob=publicationFile

It says in Section 6 subs. 3 of the Residence Act (national/D-type visa): Usually issued for up to three months (during the stay the holder shall apply for and be issued with the residence title which is appropriate for the purpose of stay).

In principle, migrants who want to stay for a longer period of time in Germany must enter the country with a visa, which gives the purpose of the stay. This means that, in order to switch from the current residence title into a new one, migrants usually need to leave the country, return to their country of origin and apply for a new visa with a new purpose of stay in order to re-enter Germany.

However, German law recognizes some exemptions, which enable migrants to change their residence title and/or purpose of stay without the obligation to leave Germany. For example, Section 5 subs. 2 of the Residence Act says that the procedure of leaving and re-entering Germany may be waived “if the prerequisites qualifying a foreigner for the granting of a residence title are met or if special circumstances relating to the individual case concerned render a subsequent visa application procedure unreasonable”.

Remember to make your request with ample time to be able to leave and reenter in case your request is not approved.