Environment:

• server 1.16.5 with fabric loader 0.11.1
• mod list:
  • bettersleeping-0.4.0.jar
  • carpet-extra-1.16.2-1.4.8.jar
  • fabric-api-0.30.0+1.16 (1).jar
  • fabric-carpet-1.16.5-1.4.26+v210210.jar
  • FabricProxy-1.4.6.jar
  • fabrictailor_fabric-1.4.0-1.16.4.jar
  • FabricTPA-1.4.1.jar
  • lithium-fabric-mc1.16.5-0.6.3.jar
  • phosphor-fabric-mc1.16.3-0.7.0+build.10.jar
• FabricProxy config:

BungeeCord = true
BungeeCordWorkaround = true
Velocity = false
allowBypassProxy = true
secret = ""

• BungeeCord
• Enabled BungeeCord version git:BungeeCord-Bootstrap:1.16-R0.5-SNAPSHOT:3d701fb:1545
• plugins:
  • Geyser 1.2.0-SNAPSHOT (git-master-b16e1d6)
• config:
  prevent_proxy_connections: false

listeners:

• query_port: 25577
  motd: '&1Another Bungee server'
  tab_list: GLOBAL_PING
  query_enabled: false
  proxy_protocol: false
  forced_hosts:
  pvp.md-5.net: lobby
  ping_passthrough: true
  priorities:
  • lobby
    bind_local_address: true
    host: 0.0.0.0:25577
    max_players: 10
    tab_size: 60
    force_default_server: false
    remote_ping_cache: -1
    network_compression_threshold: 256
    permissions:
    default:
  • bungeecord.command.server
  • bungeecord.command.list
    admin:
  • bungeecord.command.alert
  • bungeecord.command.end
  • bungeecord.command.ip
  • bungeecord.command.reload
    log_pings: true
    connection_throttle_limit: 3
    server_connect_timeout: 5000
    timeout: 30000
    player_limit: -1
    ip_forward: true
    groups:
    md_5:
  • admin
    remote_ping_timeout: 5000
    connection_throttle: 4000
    log_commands: false
    stats: 11111111-4444-ffff-22222-33333333333
    online_mode: false
    forge_support: true
    disabled_commands:
• disabledcommandhere
  servers:
  lobby:
  motd: '&1Just another BungeeCord - Forced Host'
  address: 127.0.0.1:25565
  restricted: false

Login into Fabric, mod works flamelessly.

Login into BungeeCord (Java Edition), cannot change skin and the skin is always Steve, even not the skin of the player's ID (online).

BungeeCord Bedrock(provided by Geyser) not tested yet

I'm sorry to reply late.

Login into Fabric, mod works flamelessly.

FabricTailor works only on Fabric, BungeeCord is sadly not supported really.

if I understand you correctly, your BungeeCord connects you to the Fabric server (where /skin works), but after going back to the "main" server (gosh I really need to take a look at how BC works) skin is not loaded? This is kinda expected ..?