smk: 何の苦労もないままにいきなり（厳しい）社会に出る様子。「苦労人だから、――出てきた若造とはわけが違う」

smk has a separate sense for the ぱっと in those yourei examples.
I think it's more or less covered by our sense 3.

@@ -24 +24 @@
-<gloss>suddenly (appearing, jumping out, etc.)</gloss>
+<gloss>suddenly (appearing, coming out, etc.)</gloss>

I can't really derive an edit from those comments from several days ago. Unless someone suggests something in detail, I'll just close this.

I'm not sure "jumping out" works that well (I guess it's from daijirin?)

daijisen and the jlogos dictionary (benesse) use the word 現れる, and daijisen's example is 「考えがぽっと浮かぶ」

here's another example where none of the senses really work:
バンドを解散してからソロでなかなか実績があがらず
芸能界もここまでかと言う時に
ぽっと出た、新人とのユニットの話
at first I thought it was similar to daijisen's example (if it modifies 話) but the more I think the more it seems to be a reference to ぽっと出 (if it modifies 新人)

I also tried scouring yourei.jp for more examples but the vast majority are senses 1 & 2. the remaining ones that seem to confirm my hypothesis are 東京に、ぽっと出たわたし / 田舎町からぽっと出てきた青年 / 九州の田舎からぽっと人形町の叔母の家に来て

there might be a fifth sense?

daijr, meikyo
ポッと	47,857	18.8%	
ぽっと	207,211	81.2%

I think only the last sense is vs.

@@ -5 +5 @@
-<reb>ポッと</reb>
+<reb>ぽっと</reb>
@@ -8 +8,2 @@
-<reb>ぽっと</reb>
+<reb>ポッと</reb>
+<re_inf>&sk;</re_inf>
@@ -12 +12,0 @@
-<pos>&vs;</pos>
@@ -18 +17,0 @@
-<pos>&vs;</pos>
@@ -24 +22,0 @@
-<pos>&vs;</pos>
@@ -26 +24 @@
-<gloss>suddenly (coming, appearing)</gloss>
+<gloss>suddenly (appearing, jumping out, etc.)</gloss>
@@ -32,0 +31,2 @@
+<gloss>absentmindedly</gloss>
+<gloss>vacantly</gloss>