ssh-copy-idは成功しましたが、まだパスワードプロンプトが表示されます。

仕事用PCに接続する必要がありますが、この設定を使用しています。

Host work
  User          name
  HostName      192.168.31.***
  ProxyCommand  ssh.exe p***@middle_host nc %h %p

middle_host物理デスクトップに接続する前に接続する必要がある組織ネットワーク。成功しました。ただし、ssh-copy-idパスワードを求める方法を使用してssh work接続しようとすると、middle_host会社のコンピュータには接続されません。authorized_keysチェックインしましたがmiddle_host公開鍵がそこにあります。ただし、パスワードプロンプトがなければまだ接続されません。

各種ファイルに対する権限middle_host
stat -c "%a" ~>>700
stat -c "%a" ~/.ssh/700
stat -c "%a" ~/.ssh/authorized_keys600

この回答を確認して回答に従いましたが、解決できませんでした。
公開鍵認証を使用してもSSHパスワードプロンプトが表示され続けるのはなぜですか？
ssh-copy-idは成功しましたが、まだパスワードの入力を求められます。

コメントに返信：

1. middle_host（CentOs）にrootアクセス権がないため、sshdログを確認する方法がわかりません。
2. を使用して中間ホストに接続しようとしますssh -v middle_host。Unable to negotiate with ***** port 22: no matching key exchange method found. Their offer: diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1だから試してみましたが、-oKexAlgorithms=+diffie-hellman-group1-sha1出力は次のように表示されます。

OpenSSH_8.2p1 Ubuntu-4ubuntu0.1, OpenSSL 1.1.1f  31 Mar 2020
debug1: Reading configuration data /home/koushik/.ssh/config
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: include /etc/ssh/ssh_config.d/*.conf matched no files
debug1: /etc/ssh/ssh_config line 21: Applying options for *
debug1: Connecting to ***.**.**.*** [***.**.**.***] port 22.
debug1: Connection established.
debug1: identity file /home/koushik/.ssh/id_rsa type 0
debug1: identity file /home/koushik/.ssh/id_rsa-cert type -1
debug1: identity file /home/koushik/.ssh/id_dsa type -1
debug1: identity file /home/koushik/.ssh/id_dsa-cert type -1
debug1: identity file /home/koushik/.ssh/id_ecdsa type -1
debug1: identity file /home/koushik/.ssh/id_ecdsa-cert type -1
debug1: identity file /home/koushik/.ssh/id_ecdsa_sk type -1
debug1: identity file /home/koushik/.ssh/id_ecdsa_sk-cert type -1
debug1: identity file /home/koushik/.ssh/id_ed25519 type -1
debug1: identity file /home/koushik/.ssh/id_ed25519-cert type -1
debug1: identity file /home/koushik/.ssh/id_ed25519_sk type -1
debug1: identity file /home/koushik/.ssh/id_ed25519_sk-cert type -1
debug1: identity file /home/koushik/.ssh/id_xmss type -1
debug1: identity file /home/koushik/.ssh/id_xmss-cert type -1
debug1: Local version string SSH-2.0-OpenSSH_8.2p1 Ubuntu-4ubuntu0.1
debug1: Remote protocol version 2.0, remote software version OpenSSH_4.3
debug1: match: OpenSSH_4.3 pat OpenSSH_2*,OpenSSH_3*,OpenSSH_4* compat 0x00000002
debug1: Authenticating to ***.**.**.***:22 as '****'
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug1: kex: algorithm: diffie-hellman-group1-sha1
debug1: kex: host key algorithm: ssh-rsa
debug1: kex: server->client cipher: aes128-ctr MAC: hmac-sha1 compression: none
debug1: kex: client->server cipher: aes128-ctr MAC: hmac-sha1 compression: none
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
debug1: Server host key: ssh-rsa SHA256:mDzOdf7c6GdlUbdzYqOPpD23W1gyyixbjxeUxHU0YlE
debug1: Host '***.**.**.***' is known and matches the RSA host key.
debug1: Found key in /home/koushik/.ssh/known_hosts:1
debug1: rekey out after 4294967296 blocks
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug1: SSH2_MSG_NEWKEYS received
debug1: rekey in after 4294967296 blocks
debug1: Will attempt key: /home/koushik/.ssh/id_rsa RSA SHA256:PqSSI5hAPS2zK9l+rOA7TZ01onuarhil6Fhee27+zG8
debug1: Will attempt key: /home/koushik/.ssh/id_dsa
debug1: Will attempt key: /home/koushik/.ssh/id_ecdsa
debug1: Will attempt key: /home/koushik/.ssh/id_ecdsa_sk
debug1: Will attempt key: /home/koushik/.ssh/id_ed25519
debug1: Will attempt key: /home/koushik/.ssh/id_ed25519_sk
debug1: Will attempt key: /home/koushik/.ssh/id_xmss
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey,gssapi-with-mic,password
debug1: Next authentication method: gssapi-with-mic
debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available (default cache: FILE:/tmp/krb5cc_1000)


debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available (default cache: FILE:/tmp/krb5cc_1000)


debug1: Next authentication method: publickey
debug1: Offering public key: /home/koushik/.ssh/id_rsa RSA SHA256:PqSSI5hAPS2zK9l+rOA7TZ01onuarhil6Fhee27+zG8
debug1: Server accepts key: /home/koushik/.ssh/id_rsa RSA SHA256:PqSSI5hAPS2zK9l+rOA7TZ01onuarhil6Fhee27+zG8
debug1: Authentication succeeded (publickey).
Authenticated to ***.**.**.*** ([***.**.**.***]:22).
debug1: channel 0: new [client-session]
debug1: Entering interactive session.
debug1: pledge: network
debug1: Sending environment.
debug1: Sending env LANG = C.UTF-8
Last login: Sun Feb 14 14:18:00 2021 from -----