sdkmanager tool not present in tools/bin after `apt-get install android-sdk`

This issue was originally reported at: https://answers.launchpad.net/ubuntu/+source/android-sdk-meta/+question/670196.

(1) (2) System info:

james@james-Inspiron-13-5378:~$ lsb_release -a; uname -a; apt-cache policy android-sdk
No LSB modules are available.
Distributor ID: Ubuntu
Description: Ubuntu 18.04 LTS
Release: 18.04
Codename: bionic
Linux james-Inspiron-13-5378 4.15.0-23-generic #25-Ubuntu SMP Wed May 23 18:02:16 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux
android-sdk:
  Installed: 25.0.0+8
  Candidate: 25.0.0+8
  Version table:
 *** 25.0.0+8 500
        500 http://us.archive.ubuntu.com/ubuntu bionic/universe amd64 Packages
        100 /var/lib/dpkg/status

(3) Expected: sdkmanager should be in $ANDROID_HOME/tools/bin
(4) It's not. The other tools that are listed at ___ are missing as well, in fact:

james@james-Inspiron-13-5378:/usr/lib/android-sdk$ ls tools/bin
e2fsck fsck.ext4 mkfs.ext4 resize2fs screenshot2 tune2fs

ProblemType: Bug
DistroRelease: Ubuntu 18.04
Package: android-sdk 25.0.0+8
ProcVersionSignature: Ubuntu 4.15.0-23.25-generic 4.15.18
Uname: Linux 4.15.0-23-generic x86_64
ApportVersion: 2.20.9-0ubuntu7
Architecture: amd64
CurrentDesktop: ubuntu:GNOME
Date: Fri Jun 15 19:28:11 2018
InstallationDate: Installed on 2018-06-12 (3 days ago)
InstallationMedia: Ubuntu 18.04 LTS "Bionic Beaver" - Release amd64 (20180426)
ProcEnviron:
 TERM=xterm-256color
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=en_US.UTF-8
 SHELL=/bin/bash
SourcePackage: android-sdk-meta
UpgradeStatus: No upgrade log present (probably fresh install)