Should cent coins also be abolished in Germany?

The 500 euro note has also been withdrawn from circulation. This can be done with copper money without any problems. Rounding up or down at the checkout is not a problem. It really doesn't hurt. Even the tax office often waives the decimal places. How does the accounting department deal with something like that?

Even the tax office often waives the decimal places.

Only with the assessment basis. Not with the tax anymore.

How does accounting deal with something like this?

You already have cent differences with incoming invoices in accounting for VAT because of different rounding. Some companies round VAT up or down at the individual item level and some at the final amount. If this is handled differently on both sales and purchase sides, and you have multiple items, 1-3 cents can easily add up. This leads to manual adjustment effort at least for us. Since rounding will occur regularly, I would introduce an extra line item (possibly with a separate account) for it when booking individual items for both outgoing and incoming invoices.

However, if you only book the net amount and VAT, you have no problems in this regard, regardless of rounding or not.

Who is often forgotten in such actions (abolishing cent coins) are those who have "nothing." I do not know and cannot advance with my considerations whether—for example, homeless people—are deprived of a way to somehow "get by." That, at least, speaks against it for me. I myself would also agree if copper coins no longer existed.

Some French bank manager once had all the rounding cents credited to his account. It only came to light (because no one missed them, they were just rounded off) because the transfer to his account was a huge amount in the millions. If he had done it more regularly in smaller batches, it probably would never have been discovered. I'm not sure if it's an urban legend, I can't find anything about it on the web right now. But in any case, it would be a good thing if these rounding cents were donated to charitable causes...

those who are in favor of such actions (abolishing cent coins)

It is not about abolishing all cent coins. It is only about 1 or 2 cents.

I don't know and with my considerations I also don't get any further whether - for example homeless people - are deprived of a way to somehow "get by".

What I at least see in the begging hat at main train stations are rather the 10 cents and larger coins represented. If the 3 or 4 cents in 1-cent pieces do not come in a day anymore, the donation is either the 5 cents or nothing at all.
Therefore, statistically it definitely will not make a difference.

Some French bank manager once had all rounding cents booked to his account.

That is actually a hoax.