So, a few key data points:
Current income, with the 13th salary, around €4600 monthly....
A financing in the area of around €500,000 is already very, very tight budgeted (doable, yes, but really TIGHT)
Something like that could be done if you really expect to change jobs in the next 2-3 years, and can count on at least 20% salary increases (this often happens... in my circle of friends a few years ago near Cologne it was also very tight budgeted, now with an income from a job change earning more than before with two jobs, so having a child with parental allowance is comfortably manageable).
What I would do here:
Invest money in an expert, to go through the house with them, who can well estimate when what needs to be renovated and approximate costs for that.
Then you have the complete figures on the table, what it costs (purchase + modernization that will have to be done in the next few years).
I would plan it all in, because either you can afford it immediately, or not, because then the hope would be 1) to save more money + 2) have children and have less income, which in the long run is probably the worse solution.
Also, prices continue to rise, both for real estate and for craftsmen...
When I bought a house from 1958 in 2013 and started renovating (planned €75,000 back then) we finished in 2015, and after €125,000 we stopped counting how much money had flowed in...