It depends what level of harmonic analysis you want to do.
There is the deepest, structural level of just analyzing a whole piece - I can't see the beginning, but this one probably included - as Bb: I V I
.
You can go to smaller and smaller levels of analysis.
You can analyze just the cadence of each phrase (being sure to include key labels.)
The next levels can be a bit of a mix, but you could analyze at the one bar level, probably the first beat of each bar, or possibly divisions of the measure down to the beat level. This depends a lot on the music. You would be trying to find the harmonic rhythm of the piece and analyzing the chord changes accordingly.
You're question is whether to analyze at the eighth note level. You can, but I would not. Not unless it was required by some exercise, either self-directed or from a teacher.
Personally, I ran into this problem the first time I tried to analyze Bach's first two-part invention. You could analyze that down to the sixteenth note level! I was really confused about how to do it compared to a simple SATB chorale. The solution is to analyze at the level you think is appropriate for your purpose. I'm most interested in how phrases are used to construct form. So I tend to analyze phrase cadences and then fill in important beat one changes. Also, in contrapuntal music, I tend to do Roman numeral analysis just at cadences, everything in between is contrapuntal texture far better understood via counterpoint rather than root progressions.
Also, in recent years I've been influenced by thorough bass, so I've moved away from thinking that analysis has to be Roman numeral root progression analysis (RNA.) There is an adage, I think I read it from Schoenberg, that to understand harmony you should "follow the bass".
So, finally, the moment in the music you highlighted is the final cadence, the bass is ^4 ^5 ^1
, the first beat harmony is clearly IV
, anything of ii
is weak beat decorative motion. I would analyze it IV V I
. Like Andy Bonner said in comments, I wouldn't even care about labeling the 7
on IV
. It's just a retardation of the E5
and so is melodic/contrapuntal and no real concern for RNA root progression analysis.
FWIW, it think the interesting thing is the soprano ending on ^3
instead of ^1
so the final cadence technically is not a perfect authentic cadence. Sometime pieces that end in this way on ^3
are described as "pastoral".