Bug report: stdout vs stderr

Why half of Git output goes to stdout and half to stderr? I suspect this is a bug.

Below I call `git pushbug` alias defined it the below presented config file.

$ cat .git/config 
[core]
	repositoryformatversion = 0
	filemode = true
	bare = false
	logallrefupdates = true
[remote "origin"]
	url = git@bitbucket.org:portonv/algebraic-general-topology.git
	fetch = +refs/heads/*:refs/remotes/origin/*
	pushurl = git@github.com:vporton/algebraic-general-topology.git
	pushurl = git@bitbucket.org:portonv/algebraic-general-
topology.git
[gui]
	wmstate = normal
	geometry = 1680x957+0+27 189 177
[alias]
	pushbug = !git push && git checkout prerelease && git merge
master && git push && git checkout devel && git merge prerelease &&
git push && git checkout master
[branch "master"]
	remote = origin
	merge = refs/heads/master
[branch "prerelease"]
	remote = origin
	merge = refs/heads/prerelease
[branch "devel"]
	remote = origin
	merge = refs/heads/devel

$ git pushbug 1>$HOME/t/1.txt 2>$HOME/t/2.txt
$ cat ~/t/1.txt 
Your branch is up-to-date with 'origin/prerelease'.
Updating ac492a4..c55d1b5
Fast-forward
 chap-sides.tex | 15 +++++++++++++--
 1 file changed, 13 insertions(+), 2 deletions(-)
Your branch is up-to-date with 'origin/devel'.
Updating ac492a4..c55d1b5
Fast-forward
 chap-sides.tex | 15 +++++++++++++--
 1 file changed, 13 insertions(+), 2 deletions(-)
Your branch is up-to-date with 'origin/master'.
$ cat ~/t/2.txt 
To git@github.com:vporton/algebraic-general-topology.git
   ac492a4..c55d1b5  master -> master
To git@bitbucket.org:portonv/algebraic-general-topology.git
   ac492a4..c55d1b5  master -> master
Switched to branch 'prerelease'
To git@github.com:vporton/algebraic-general-topology.git
   ac492a4..c55d1b5  prerelease -> prerelease
remote: 
remote: Create pull request for prerelease:        
remote:   https://bitbucket.org/portonv/algebraic-general-topology/pull
-requests/new?source=prerelease&t=1        
remote: 
To git@bitbucket.org:portonv/algebraic-general-topology.git
   ac492a4..c55d1b5  prerelease -> prerelease
Switched to branch 'devel'
To git@github.com:vporton/algebraic-general-topology.git
   ac492a4..c55d1b5  devel -> devel
remote: 
remote: Create pull request for devel:        
remote:   https://bitbucket.org/portonv/algebraic-general-topology/pull
-requests/new?source=devel&t=1        
remote: 
To git@bitbucket.org:portonv/algebraic-general-topology.git
   ac492a4..c55d1b5  devel -> devel
Switched to branch 'master'