Simply put:
A partial default judgment means your claim is only partly valid and partly invalid based solely on the evaluation of the complaint. If the defendant now files an objection, the proceedings continue as usual. If not, an appeal can only be filed against the judgment.
After the judgment becomes final (or even now, although this is generally not advisable), the judgment can be enforced, i.e., you can, if necessary, enforce the release of the escrow account with the help of a bailiff.
The procedural costs are divided according to the ratio of the claim to the ruling, since your claim was not entirely successful. As the plaintiff, you had to pay an advance, which you can partially claim from the defendant. This includes not only the court costs but also the costs for your lawyer. These costs are determined by the court and can then also be claimed from the opponent. However, your lawyer takes care of this.