I'm installing 3/4" hardwood oak in my den. Subfloor looks to be some sort of OSB type of 3/4" plywood.
The hallway already has hardwood floor, going right up to the doorway.
I was planning on using a silicone moisture barrier (Roberts, white) underneath the flooring. Under the den is a finished heated basement.

As seen in this image: https://drive.google.com/file/d/1TuMMHAmFBLA4wllOM6cnSJl0VPxxBw2j/view?usp=sharing, the existing hallway hardwood floor ends with a terminating cross piece (as a visual threshold I guess).

The open end (vertical edge) of this piece is flat (no tongue or groove).
I was planning to install the new hardwood floor right up against this cross piece.
I was planning on leaving an inch or so gap in the moisture barrier (along this piece) and put a bead of glue (urethane based) along this piece where it meets the subfloor. The motive is to minimize risk movement and squeaks.

Does this sound reasonable?

At the other end of hallway is the dining room, whose doorway also has a similar cross terminating piece, and the existing hardwood goes right up against it, as seen in the other image. https://drive.google.com/file/d/1qUpc6OlVrW-AwbkFhsHz9HCVWKbM86tG/view?usp=sharing
This tells me it's OK to not have an expansion gap between the hallway and the den (because that's what they did between the hallway and dining room). Sound reasonable?

The glue I was going to use is: LOCTITE PL Premium 10-fl oz Polyurethane Construction Adhesive

let me know if this plan is OK or not

It is usual to not have any expansion gap between rooms. When laying a new floor against an older floor you have the moisture content of the older floor to compare with a new floor before you do the installation. If the new floor is close to the old floors moisture content it will not expand or contract much if at all. This close moisture content wood can be laid tight against the old floor. If the moisture content is less than the old floor you can use a table to find the average difference in width for each percent of moisture content difference compared to the old floor with a table that has the average expansion for a two and a quarter inch width piece of hardwood flooring. The flooring will not expand lengthwise, but will expand or shrink widthwise with a difference of moisture content. To be sure, you can purchase a moisture meter on line or at Harbor Freight. The moisture content of the wood does not need to be an exact number, just compare the two of them to check if they are close.