BDAG essentially comments on this verse in Acts 10:36Acts 10:36 by suggesting its meaning is:
Since according to the prophets, peace will be an essential characteristic of the messianic kingdom (...), Christian thought also frequently regards εἰρήνη as nearly synonymous with messianic salvation (Isa 52:7), Acts 10:36; Rom 10:15 v.1; Eph 2:17; τοῦ εὐαγγελίου τῆς εἰρήνης Eph 6:15. ...
See also John 16:33, Rom 5:1, John 14:27, 2 Thess 3:16b, etc.
Ellicott:
Preaching peace.—Better, as reproducing with the Greek the thought and language of Isaiah 52:7, preaching glad tidings of peace.
Matthew Henry:
The purport of this word was, that God by it published the good tidings of peace by Jesus Christ. They knew the several matters of fact relating to the gospel. They knew the baptism of repentance which John preached. Let them know that this Jesus Christ, by whom peace is made between God and man, is Lord of all; not only as over all, God blessed for evermore, but as Mediator.
Barnes:
Peace - This word ... is used here in a wider sense, to denote "peace or reconciliation with God." He announced the way by which man might be reconciled to God, and might find peace.
Gill:
preaching peace by Jesus Christ: that word preached, or the apostles in the ministry of it preached; or rather God, who sent the word by them, preached through them the doctrine of peace and reconciliation, by the blood of Christ; and this being so principal a doctrine of the Gospel, the whole is called from it, the Gospel of peace, and the word of reconciliation: by "peace" here is meant ... peace with God, which was broken by the sin of man, which filled his mind with enmity to God; and now he is incapable of restoring it, and reconciling himself to God;
See also Is the term שָׁלֹום (peace) in Isaiah 53:5 usually misunderstood?