На той же странице на berlin_de есть "Fact sheet for foreign workers" И там написано так:
B) If you have been issued an EU Blue Card in accordance with Section 18b (2) of the Residence Act without the approval of the Federal Employment Agency: In this case, the ancillary stipulation „Beschäftigung gemäß § 18b Abs. 2 S. 1 AufenthG erlaubt“ (‘employment in accordance with § 18b par. 2 sentence 1 AufenthG permitted’) is entered on your extension page to the electronic residence permit. You are therefore permitted to engage in any employment appropriate for your qualifications, provided that in the current calendar year 2023 you receive a minimum gross income of €4,866.67 per month, with reference to the regular salary agreed in the employment contract – variable special payments of any kind should not be included. If you fulfil these criteria, please send us your new employment contract so that we can review it. A change of your EU Blue Card is not necessary and will only be carried out when it has to be extended. Until then, if your employer or other public authorities or offices have enquiries, please present them with this fact sheet.
Так что да, в вашем случае разрешение не требуется