Matthew, there's a terrific QGIS plugin that does exactly what you want. I've used it successfully for some time. It's called Points to Paths (note the plural Paths), and is only available at QGIS version 2.x (don't stop reading - hear me out!). It is far more capable than the 3.x Points to Path (note the singular Path) that you've tried without success.
Since Points to Paths hasn't been updated yet for 3.x, you'll have to install a separate QGIS 2.x version on your computer, but I think that it's well worth the small effort. Fortunately, 2.x and 3.x seem to play well together.
Older Mac QGIS installs can be downloaded here:
and older Windows installs here:
After installing 2.x (I use 2.18.28, the last 2.x release), install the Points to Paths plugin. A few notes on its use:
"Point Group Field": Use this if your point data is organized into unique groups, such as specific airline flights.
"Point Order Field": This field contains the point sequence that, in turn, dictates the resulting line direction. Using the airline flight example, this would be a time stamp for each point along the flight's route. Think GPS breadcrumbs.
If your "Point Order Field" is formatted as text, and it contains date and/or time info (such as 2019-10-01 19:24:30) you need to specify that format in the "Date Format" fill-in box. Using my year-month-day hour:minute:second example, you would enter %Y-%m-%d %H:%M:%S I don't know why month and day are lower-case.
Check the "Line per Vertex" box. This is critical! When checked, a separate line segment is created for each unique "Point Order Field" value, and (this is where the magic happens) the output line shapefile includes two attribute fields containing the beginning and ending values, respectively, from the point layer's "Point Order Field". You can now join the line layer to the point layer, and then create/calculate additional line layer fields, populating them from the point layer` (airspeed, altitude...). Voila - your line layer now carries the correct point attribute info!
This is a really useful tool (there's even no Arc Desktop equivalent), and I hope it is quickly added to the 3.x plugin repository. Until then, however, I'm keeping a separate 2.x installation on my computer.