For a single line text (w/o any StyleOverrides), the "oPickedDrawingNote.Text" and "oPickedDrawingNote.FormattedText" is the same
That is the reason why your code initially works the first time. After the code ran, Text and FormattedText won't be the same anymore
For multi-line text (w/o any StyleOverrides), the "oPickedDrawingNote.Text" and "oPickedDrawingNote.FormattedText" is NOT the same .
FormattedText has additional line breaks "<Br\> inside that isn't shown in Text property.
As for a solution, you can try below code
Dim oDrawDoc As Inventor.DrawingDocument = ThisApplication.ActiveDocument
Dim oPickedDrawingNote As Inventor.DrawingNote = ThisApplication.CommandManager.Pick(SelectionFilterEnum.kDrawingNoteFilter, "Select text")
'Logger.Info("Method2")
Dim eText As String = oPickedDrawingNote.FormattedText
Logger.Info(eText)
'Remove All the styleoverrides
Dim sText As String() = eText.Split("<StyleOverride ", StringSplitOptions.RemoveEmptyEntries)
For Each subText In sText
Dim sOldStyle As String = Left(subText, InStr(subText, ">") -1)
eText = eText.Replace("<StyleOverride " & sOldStyle & ">", String.Empty)
eText = eText.Replace("</StyleOverride>", String.Empty)
Next
'Apply New Style Overrides
oPickedDrawingNote.FormattedText = "<StyleOverride Font='Tahoma' FontSize='0.3' Bold='False' Underline='False'>" & eText & "</StyleOverride>"
I'm not too much familiar with the XML formatting, but it seems it is smart enough to apply the styleoverrides after the line breaks.
as an example:

the Formatted text of that is
TEXT<Br/>TEST
after the rule, the expected value of the FormattedText is
<StyleOverride Font='Tahoma' FontSize='0.3' Bold='False' Underline='False'>TEXT<Br/>TEST</StyleOverride>
but surprising enough, the FormattedText Property is able to "correct" it to
<StyleOverride Font='Tahoma' FontSize='0.3'>TEXT</StyleOverride><Br/><StyleOverride Font='Tahoma' FontSize='0.3'>TEST</StyleOverride>
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btw, I think it cannot do math expressions for the font size in XML format directly. so have to separate it (or just assign the computed value)
so instead of doing it as
oPickedDrawingNote.FormattedText = "<StyleOverride Font='Tahoma' FontSize='0.12*2.54' Bold='False' Underline='False'>" & eText & "</StyleOverride>"
do it as
oPickedDrawingNote.FormattedText = "<StyleOverride Font='Tahoma' FontSize='" & 0.12*2.54 & "' Bold='False' Underline='False'>" & eText & "</StyleOverride>"