but it shouldn’t be just military.

Already the case. Quoth Article 12a GG:

1. Men who have attained the age of eighteen may be required to serve in the Armed Forces, in the Federal Border Police, or in a civil defence organisation.

2. Any person who, on grounds of conscience, refuses to render military service involving the use of arms may be required to perform alternative service. The duration of alternative service shall not exceed that of military service. Details shall be regulated by a law, which shall not interfere with the freedom to make a decision in accordance with the dictates of conscience and which shall also provide for the possibility of alternative service not connected with units of the Armed Forces or of the Federal Border Police.

3. Persons liable to compulsory military service who are not called upon to render service pursuant to paragraph (1) or (2) of this Article may, when a state of defence is in effect, be assigned by or pursuant to a law to employment involving civilian services for defence purposes, including the protection of the civilian population; they may be assigned to public employment only for the purpose of discharging police functions or such other sovereign functions of public administration as can be discharged only by persons employed in the public service. The employment contemplated by the first sentence of this paragraph may include services within the Armed Forces, in the provision of military supplies or with public administrative authorities; assignments to employment connected with supplying and servicing the civilian population shall be permissible only to meet their basic requirements or to guarantee their safety.

4. If, during a state of defence, the need for civilian services in the civilian health system or in stationary military hospitals cannot be met on a voluntary basis, women between the age of eighteen and fifty-five may be called upon to render such services by or pursuant to a law. Under no circumstances may they be required to render service involving the use of arms.

5. Prior to the existence of a state of defence, assignments under paragraph (3) of this Article may be made only if the requirements of paragraph (1) of Article 80a are met. In preparation for the provision of services under paragraph (3) of this Article that demand special knowledge or skills, participation in training courses may be required by or pursuant to a law. In this case the first sentence of this paragraph shall not apply.

6. If, during a state of defence, the need for workers in the areas specified in the second sentence of paragraph (3) of this Article cannot be met on a voluntary basis, the right of German citizens to abandon their occupation or place of employment may be restricted by or pursuant to a law in order to meet this need. Prior to the existence of a state of defence, the first sentence of paragraph (5) of this Article shall apply, mutatis mutandis.

The short of the story is that the draft was never abolished, instead they suspended its application. Constitutionality-wise what became an issue is that the army would only call up a fraction of eligible people, if we re-do all this they probably have to make sure to call up everyone and then funnel lots into other areas as the military doesn't even want that many people. Civil defence certainly won't mind.

internship at a town planning and engineering service, to litter pickup, to the military.

It's generally either medical services (EMT, distributing food for the elderly, various other stuff) or civil defence. If you're picky and engaged you could even get a gig counting birds as certain nature preservation efforts and data collection count as civil defence (to do catastrophe relief it helps to have an eye on nature), don't think they'll take a random slob over someone who actually wants to be an ornithologist, though.

What we really shouldn't be re-introducing is that "distribute food for the elderly" stuff. Zivis were always a way for the system to depress wages in the sector and now noone wants to be a nurse for the elderly. I mean if people really want to sure go ahead but we shouldn't be funnelling people there on a default path, that should probably some big-picture civil defence stuff, definitely including evacuations if only because it's way easier to evacuate a city when a lot of people there already know how to do it.