Back to multiple "etc", but it's hard to avoid that.

I think this is clearer.

@@ -12,2 +12,2 @@
-<s_inf>esp. 第〜弾, as in 第２弾 etc.</s_inf>
-<gloss>counter for parts (e.g. of story or series), events, projects, etc.</gloss>
+<s_inf>esp. as 第〜弾, e.g. 第２弾</s_inf>
+<gloss>counter for parts, stages, installments, etc. (of a story, series, project, campaign, etc.)</gloss>

Maybe better.

@@ -13 +13 @@
-<gloss>counter for parts (of a story, series, etc.), events, projects, etc.</gloss>
+<gloss>counter for parts (e.g. of story or series), events, projects, etc.</gloss>

koj
daijs:
１ たま。弾丸。また、それを数える語。
２ （弾丸にたとえて、多く接尾語的に用いる）
㋐次々と打ち出す企画や計画、作品などを数える語。「バーゲンセール第1弾」「シリーズ第3弾の映画」

https://www.tofugu.com/japanese/japanese-counters-list/

Not sure how I feel about the nested "etc"s.

@@ -13 +13,5 @@
-<gloss>counter for parts (of a story, etc.)</gloss>
+<gloss>counter for parts (of a story, series, etc.), events, projects, etc.</gloss>
+</sense>
+<sense>
+<pos>&ctr;</pos>
+<gloss>counter for bullets</gloss>

I don't think that's 弾 being used as a suffix - it's just the regular use of a kanji in Japanese kango morphology. Unidic. which is a major morpheme lexicon, shows 砲弾, 銃弾 and 防弾 as free-standing morphemes; not as noun+suffix formations.

@@ -15,4 +14,0 @@
-<sense>
-<pos>&n-suf;</pos>
-<gloss>bullet</gloss>
-</sense>