How to check if a pull request on GitHub has conflicts using a script?

Here is how to pipe it without a shell loop, and parse JSON natively, either with gh api -q built-in jq query, or jq itself.

#!/usr/bin/env sh

REPOSITORY_NAME=
OWNER=

gh api -H "Accept: application/vnd.github+json" \
  "repos/${OWNER}/${REPOSITORY_NAME}/pulls" --cache 1h |
  jq -j --arg curbranch "$(git rev-parse --abbrev-ref HEAD)" \
  '
.[] | select(
  (.base.ref == $curbranch) and
  (.state == "open") and
  (.draft == false)
) | .number | tostring + "\u0000"
' |
  xargs -0 -I{} \
    gh api -H "Accept: application/vnd.github+json" \
    "repos/${OWNER}/${REPOSITORY_NAME}/pulls/{}" --cache 1h \
    -q '
"PR #" + (.number | tostring) + ": " +
.title + " is " +
if .mergeable != false then "mergeable" else "not mergeable" end
'

Altenatively using a while read -r loop instead of xargs which seems problematic in some Windows environment:

gh api -H "Accept: application/vnd.github+json" \
  "repos/${OWNER}/${REPOSITORY_NAME}/pulls" --cache 1h |
  jq -r --arg curbranch "$(git rev-parse --abbrev-ref HEAD)" \
  '
.[] | select(
  (.base.ref == $curbranch) and
  (.state == "open") and
  (.draft != true)
) | .number
' | while read -r pr; do
    gh api -H "Accept: application/vnd.github+json" \
    "repos/${OWNER}/${REPOSITORY_NAME}/pulls/${pr}" --cache 1h \
    -q '
"PR #" + (.number | tostring) + ": " +
.title + " is " +
if .mergeable != false then "mergeable" else "not mergeable" end
'
done

So I wanted to share my solution which is much "cleaner" than what I wrote in the question. I simply used GitHub API to retrieve the "mergeable" state information of the pull request. This does not require me to do any local merges and discards to search for conflict-identifying strings such as ">>>>>>>" etc.

#!/bin/bash    
OWNER="GitHub_UserName" #your github user name or organization name - whoever owns the repository
REPOSITORY_NAME="Your_Repo_Name"
PR_List=$(gh pr list) #Get list of pull requests of the repository
Current_Branch=$(git rev-parse --abbrev-ref HEAD) #get the current branch name
if [[ $(grep "$Current_Branch" <<< "$PR_List") ]]; then #If true then there exists a PR for this branch in the repository 
        #Get the line of the pull request from the list:
        PR_Line=$(grep "$Current_Branch" <<< "$PR_List")
        
        #Get the specific numerical ID of the pull request
        PR_ID=$(awk '{print $1}' <<< "$PR_Line")    #taken from https://stackoverflow.com/a/36736249/4441211

        #now get all the PR information from GitHub:
        pr_data=$(gh api -H "Accept: application/vnd.github+json" repos/$OWNER/$REPOSITORY_NAME/pulls/$PR_ID)

        #Now extract the specific "mergeable" state of the PR and then check it:
        mergeable_row=$(grep "mergeable" <<< "$pr_data")
        mergeable_string=$(echo "$mergeable_row" | awk -F 'mergeable":' '{printf $NF}')
        mergeable_state=$(echo "$mergeable_string" | cut -d',' -f 1)
        echo "Mergeable = $mergeable_state" #for debug
        if [ "$mergeable_state" == "false" ]; then
            MergeIssuesFound="yes"
            echo "Pull Request in repository $REPOSITORY_NAME is NOT mergeable"
        else
            MergeIssuesFound="no"
            echo "Pull Request in repository $REPOSITORY_NAME is mergeable"
        fi
fi