This simple shell script will find the closest tex root file upwards from a given location.

findTexRoot.sh

#!/bin/bash

# Usage example:
# if roottex=$(~/findroot.sh .); then; echo $roottex; else; echo No root found;fi

# This constant determines how many directories will be searched.
# A value of 0 will result in no searching at all, 1 will search the directory of the given file or the given directory
SEARCHDEPTH=3

## This part is only parameter validation
function showUsage {
    echo USAGE: $0 FILENAME
    echo "       This script will find the nearest Latex root document to the given location"
    echo "       It will only search in parent directories, never in child directories"
}

# Check if something other than exactly one argument was given
if (( $# != 1)); then
    (>&2 showUsage)
    exit 1
fi

# Check if the given file does NOT exist
if [[ ! -e $1 ]]; then
    (>&2 echo $1: File not found.)
    (>&2 echo)
    (>&2 showUsage)
    exit 1
fi


## Start of actual logic

TEXFILE="$(realpath "$1")"

# Find the directory to start the search
# If the supplied path points to a file, start at the directory of that file
if [[ -f $TEXFILE ]]; then
    TEXDIR="$(dirname "$TEXFILE")"
else
    TEXDIR="$TEXFILE"
fi

# The searchTexRoot function takes 2 parameters:
# $1: The directory to search
# $2: The remaining search depth.
function searchTexRoot {
    if (($2 > 0)); then
        # Use find to find all .tex files in the current directory
        # -maxdepth 1 essentially disables directory recursion
        files=$(find "$1" -maxdepth 1 -path "*.tex" -print)
        # Iterate over all files which where found
        for f in $files; do
            # Use grep to find a "\begin{document}" inside of the tex file.
            # -q disables output and makes grep exit with 0 on the first hit
            # -F makes grep interpret the given pattern as a fixed string
            if grep -qF "\begin{document}" "$f"; then
                echo $f
                # Exit after the first hit to prevent outputting multiple files
                exit 0
            fi
        done

        # Continue to search as long as the directory name changes
        nextdir="$(dirname "$1")"
        if [[ "$nextdir" != "$1" ]]; then
            searchTexRoot "$nextdir" $(($2 - 1))
        fi
    fi
}

# Start the recursive search
searchTexRoot "$TEXDIR" $SEARCHDEPTH
exit 1