ωστε introduces consequence, not basis

As a result indicates that what follows in verses 13–14 is the
consequence of the progress of the gospel (cf. Bruce “the upshot of it
all has been this”). Even though the phrase has been discarded by many
translators, it is best to have it for a better connection.

Loh, I.-J., & Nida, E. A. (1995). A handbook on Paul’s letter to the
Philippians (p. 20). New York: United Bible Societies.

Also, I’ve made it plain that there are two results by combining the
sentences.

51-PHP/01.usfm

@@ -24,8 +24,8 @@
 \s5
 \p
 \v 12 Now I want you to know, brothers, that the things that happened to me have advanced the progress of the gospel very much.
-\v 13 This is because my chains in Christ became known throughout the whole palace guard and to everyone else.
-\v 14 And most of the brothers in the Lord have been more persuaded because of my chains to dare to speak the word fearlessly. 
+\v 13 As a result, my chains in Christ became known throughout the whole palace guard and to everyone else,
+\v 14 and most of the brothers in the Lord have been more persuaded because of my chains to dare to speak the word fearlessly. 
 
 \s5
 \v 15 Some indeed even proclaim Christ out of envy and strife, and also others out of good will.