HMRC Admin 25,
While what you say is correct, you need to read what Roger Williams actually asks, "In these circumstances can my UK Government Pension be taken into account by the German tax authorities to determine how much tax I pay in Germany?" That is not the same as "Can my Teachers' Pension be taxed by Germany?"
The answer to his question is "yes", because of Article 23(1)(d) in the DTA, and section 32b of the German Income Tax Act, which I quote above. Germany does not tax the income but takes it into account when setting the rate of tax on the income they do tax. I know of a number of people who have found themselves "in correspondence" with their German tax office for failing to report UK income that is exempted from tax in Germany by the DTA - a potentially expensive mistake!
For example, if a German resident (without citizenship) had income of 50,000€ arising in Germany, then for 2024 they will pay 10,906€ tax - an effective tax rate of 21 .81% (the German system is not a slab system like the UK's). If, instead, they had 30,000€ arising in Germany and a 20,000€ UK Government Service pension, taxable only in the UK, their 30,000€ would NOT be taxed at the rate applicable to 30,000€ (14.82%) but at the rate applicable to 50,000€ (21.81%). They would therefore pay tax of 6,543€, not 4,446€ - a difference of 2.097€.
This is not the same as taxing the income in Germany: it is the German government saying that a person's tax rate should be measured by reference to their worldwide income, even if some of that income is exempt from tax under a double tax agreement. This is why the income is reported on a special Annex to the tax return.
In reality this is a matter for Roger to take up with his German tax adviser, or the German tax office, as Germany is doing no more than the DTA and their domestic legislation provide for.
I cannot post links but he may like to search his tax authority website for "Progressionsvorbehalt-Rechner" (it is certainly on the Bayern Tax Office site) where he will be able to see the impact on his German tax rate of having a UK Government Service pension, or UK property rental income, or a UK State Pension for that matter...