Shadows in the afternoon/early evening through the adjacent forest

I find it beautiful with the trees. I would buy it immediately if everything else fits. Since summers will probably get hotter and more extreme anyway, that's just another plus. And who sits out in the blazing sun for long? Usually, the blinds are then closed, the umbrella opened. And you do have sun. I find this partial shading ideal. Honestly, in summer I only run from shadow to shadow when it’s 30° or more and I am grateful for every tree that casts shade for us.

Is the property now purchased?

Kindergarten is being newly built about 500 m away, an elementary school is already in the immediate vicinity,

That would give me far more to think about than the trees – I think they’re great.

But a school and a kindergarten that close???
Screaming hordes of children are one thing – I don’t find that so bad and it’s over by evening anyway – but the hordes of SUV-owning parents who have to drive their offspring there and pick them up again in the afternoon (does anyone still walk to school or kindergarten with their kids nowadays???), I wouldn’t be up for that.

Nice that you now perceive children as

not (...) so bad

But why does the topic keep triggering you, even though it doesn't affect you at all? Also, factually, childcare facilities mean: evenings = quiet, weekends = quiet, holidays = quiet... the exact opposite of restaurants, leisure facilities, various businesses, etc.

(Does anyone still walk to school or kindergarten with their kids today???

Elementary school children can walk or bike by themselves. Nowadays, however, they would very likely be run over by SUVs...

I personally just wouldn't be interested in SUV traffic jams in front of the school and kindergarten every WORKday in the morning and after school/kindergarten ends.

An acquaintance of mine lives in Munich opposite a (smaller) school in a play street - she sometimes has trouble getting out of her garage in the morning because the street is almost completely parked with parents' cars (not just SUVs, that was a cliché, I admit).
Unfortunately, this has now become quite a valid problem worth thinking about.

I also wouldn't necessarily want to buy a property next to a kindergarten or a school - it has a noticeable impact on resale prices. You can argue about whether this is child-friendly or not, but it is what it is.
If you don’t have money to spare, you should simply keep such conditions in mind (even if it’s only to be able to negotiate the price down if necessary).