Migrate EL406 and BioShake docs to manufacturer-based layout

Move plate washer docs from 00_liquid-handling/plate-washing/ to
agilent/biotek/el406/ and heater-shaker docs from
01_material-handling/heating_shaking/ to qinstruments/bioshake/.
Add Manufacturers toctree section with manufacturer-level indexes.
Include migration guide at repo root for future device migrations.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: rickwierenga

docs/user_guide/00_liquid-handling/_liquid-handling.rst

@@ -19,7 +19,6 @@ Examples:
    hamilton-prep/_hamilton-prep
    opentrons/ot2/ot2
    tecan-evo/_tecan-evo
-   plate-washing/plate-washing
    pumps/_pumps
    moving-channels-around
    tutorial_tip_inventory_consolidation

docs/user_guide/00_liquid-handling/plate-washing/biotek-el406.ipynb

@@ -18,12 +18,11 @@ PyLabRobot supports the following heater shakers:
 - Inheco ThermoShake (should have the same API as RM)
 - Inheco ThermoShake AC (should have the same API as RM)
 - Hamilton Heater Shaker (tested)
-- QInstruments BioShake (3000 elmm, 5000 elm, and D30-T elm tested)
+- QInstruments BioShake (3000 elm, 5000 elm, and D30-T elm tested)
 
 ```{toctree}
 :maxdepth: 1
 
 Inheco ThermoShake <inheco>
 Hamilton Heater Shaker <hamilton>
-QInstruments BioShake <qinstruments>
 ```