Haven't noticed that in my searches yet so haven't needed to add any blocking for that persuasion message. Do you still see it with these filters?
! https://news.ycombinator.com/item?id=21860328
booking.com##.soldout_property
booking.com##.sr_rooms_left_wrap.only_x_left
booking.com##.lastbooking
booking.com##.sr--x-times-booked
booking.com##.in-high-demand-not-scarce
booking.com##.top_scarcity
booking.com##.hp-rt-just-booked
booking.com##.cheapest_banner_content > *
booking.com##.hp-social_proof
booking.com##.fe_banner__red.fe_banner__w-icon.fe_banner__scale_small.fe_banner
booking.com##.urgency_message_x_people.urgency_message_red
booking.com##.rackrate
booking.com##.urgency_message_red.altHotels_most_recent_booking
booking.com##.fe_banner__w-icon-large.fe_banner__w-icon.fe_banner
booking.com##.smaller-low-av-msg_wrapper
booking.com##.small_warning.wxp-sr-banner.js-wxp-sr-banner
booking.com##.lock-price-banner--no-button.lock-price-banner.bui-u-bleed\@small.bui-alert--large.bui-alert--success.bui-alert
Apart from these, I use some additional ublock filters to block some of their tracking that I am not ok with. $removeparam=/^(error_url|ac_suggestion_theme_list_length|ac_suggestion_list_length|search_pageview_id|ac_click_type|ac_langcode|ac_position|ss_raw|from_sf|is_ski_area|src|sb_lp|sb|search_selected|srpvid|click_from_logo|ss|ssne|ssne_untouched|b_h4u_keep_filters|aid|label|all_sr_blocks|highlighted_blocks|ucfs|arphpl|hpos|hapos|matching_block_id|from|tpi_r|sr_order|srepoch|sr_pri_blocks|atlas_src|place_types)/,domain=booking.com
$removeparam=/sid=.\*;BBOX/,domain=booking.com
||www.booking.com/c360/v1/track
||www.booking.com/fl/exposed
||booking.com/personalisationinfra/track_behaviour_property
||booking.com/has_seen_review_list
Note that these may result in you receiving some higher prices by removing some referrer info. If you do see that happening, feel free to remove the offending config if the price difference is significant for you. I usually don't bother for differences of < $10 (price displayed on the search page vs the property page).