It seems the mistake I made was not wrapping my <Style>
's inside a <Styles>
tag. After doing that it seems to work. Kind of an embarrassing thing to find out directly after posting the question.
Working now:
<?xml version="1.0" encoding="utf-8"?>
<ScintillaNET>
<Language Name="65c816 asm">
<Indentation TabWidth="4"/>
<Lexer LineCommentPrefix=";" >
<Keywords List="0" Inherit="False">
adc adc and asl bcc bcs beq bit bmi bne bpl
bra brk brl bvc bvs clc cld cli clv cmp cop
cpx cpy dec dex dey eor inc inx iny jmp jsr
lda ldx ldy lsr mvn mvp nop ora pea pei per
pha phb phd phk php phx phy pla plb pld plp
plx ply rep rol ror rti rtl rts sbc sec sed
sei sep sta stp stx sty stz tax tay tcd tcs
tdc trb tsb tsc tsx txa txs txy tya tyx wai
wdm xba xce
</Keywords>
</Lexer>
<Styles>
<Style Name="CHARACTER" ForeColor="#00AAFF"/>
<Style Name="NUMBER" ForeColor="#00AA00"/>
</Styles>
</Language>
</ScintillaNET>