These are the most important points and very well explained!
You should now find out what you can afford at most (bank), want (you), or have to (region) and also inform yourself comprehensively now to define your requirements: what features should the house have, location, plot, floor plan, age, renovation status, etc.
When you are at that stage and HAVE found THE house, you should be able to quickly and solidly commit without much hesitation, otherwise someone else will buy it: bank commitment, contact with appraiser, quick estimation of renovation costs.
And yes: when you know exactly what you can afford and even want, know some renovation costs, and know how to implement your wishes in a used property (e.g. wall breakthrough, bathroom renovation, energy-saving implementations), only then can you relatively quickly commit to buying the house.
You call the agent, make an appointment, get your first impression, talk, plan and calculate (calculation = house price or bid plus additional purchase costs plus renovations), so that you can tell the agent the next day: we'll take it. Then you go to a bank or another lender you trust (prerequisite: your limit and conditions are no longer unknown to you), it doesn’t have to be your online bank, you take your salary and house documents as well as the calculation with you and say: it’s urgent, we need a loan.
And yes: the agent wants the bank commitment as soon as possible that you can actually get this amount. It therefore makes sense to get a bank already on board that knows you and can then also provide a written bank commitment immediately after an appraisal. After that, you have enough time to inspect the house with an expert and identify defects. You mention these defects to the agent and only offer 70-90% of the favored house price accordingly (provided that the sales price has already been checked regarding the realistic sales price). A bit generalized.
If you don’t know quickly what you want and can do with an interesting property and don’t get this written commitment, it may be that someone else is faster.